Acceso
Prima
Hogar Banco de preguntas Matemáticas Trigonometría
Pregunta
upstudy study bank question image url

\( \frac { 1 } { \sin x } - \sin x = \frac { \cos x } { 1 + \operatorname { cin } x } \)

Ask by Donnelly Parry. in South Africa
Mar 11,2025

Solución de inteligencia artificial de Upstudy

Respuesta verificada por el tutor

Responder

Please clarify the equation by confirming if \(\operatorname{cin} x\) is intended to be \(\operatorname{csc} x\).

Solución

¡Inicia sesión para desbloquear respuestas gratis!

Una plataforma de aprendizaje en la que confían millones de estudiantes y profesores reales.

star-icon Descubrir

Respondido por UpStudy AI y revisado por un tutor profesional

Extra Insights

Let's explore the equation you've given! The left-hand side combines a cosecant function \( \frac{1}{\sin x} \) with the sine function itself, which can be rewritten for better analysis. Similarly, the right side consists of cosine and a function involving the sine, which seems to have a typo; did you mean to write "sin" instead of "cin"? If so, the equation might be solvable. To find common ground, it’s helpful to express both sides in terms of sine and cosine only. This makes it easier to isolate variables or simplify the equation, guiding you toward potential solutions. Remember to consider the restrictions imposed by the functions involved, like avoiding values where sine equals zero! Now, if you found the intricacies of this equation intriguing, you might also enjoy checking out trigonometric identities! They’re foundational in simplifying and solving such expressions, making trigonometry not just a tool for calculation but a fascinating puzzle of relations between angles and lengths. Dive into identities like Pythagorean, sum and difference, or double angle formulas to see the enchanting connections!

preguntas relacionadas

STION 6 Without using a calculator, simplify the following expression to a single trigonometric term: \( \frac{\sin 10^{\circ}}{\cos 440^{\circ}}+\tan \left(360^{\circ}-\theta\right) \cdot \sin 2 \theta \) Given: \( \sin \left(60^{\circ}+2 x\right)+\sin \left(60^{\circ}-2 x\right) \) 6.2 .1 \( 6.2 .2 \quad \) Calculate the value of \( k \) if \( \sin \left(60^{\circ}+2 x\right)+\sin \left(60^{\circ}-2 x\right)=k \cos 2 x \). If \( \cos x=\sqrt{t} \), without using a calculator, determine the value of \( \tan 60^{\circ}\left[\sin \left(60^{\circ}+2 x\right)+\sin \left(60^{\circ}-2 x\right)\right] \) in terms of \( t \).
Trigonometría South Africa Mar 12, 2025
шамданыз: \( \left(\operatorname{ctg} \alpha+\frac{\sin \alpha}{1+\cos \alpha}\right)^{2}-\operatorname{ctg}^{2} \alpha \)
Trigonometría Kazakhstan Mar 12, 2025
6. Rezolvaṭi următoarele ecuatii trigonometrice elementare: \( \begin{array}{ll}\text { a) } \sin 5 x=\sin 3 x ; & \text { b) } \cos x=\cos 4 x \\ \text { c) } \cos 5 x=-\sin 3 x ; & \text { d) } \operatorname{tg} 4 x=\operatorname{ctg}\left(3 x+\frac{\pi}{4}\right) ; \\ \begin{array}{ll}\text { e) } \sin \left(\frac{3 \pi}{2}+x\right)+\cos 3 x=0 ; & \text { f) } \cos \left(\frac{3 x}{2}+\frac{\pi}{4}\right)+\sin \left(\frac{2 x}{3}-\frac{\pi}{4}\right)=0\end{array} \\ \text { 7. Rezolvați următoarele ecuații trigonometrice elementare: } \\ \begin{array}{lll}\text { a) } \sin x=\sin 7 x ; & \text { b) }-\sin 2 x=\sin x ; & \text { e) } \operatorname{tg} 4 x=\operatorname{tg} 2 x ;\end{array} & \text { c) } \cos 4 x=\cos 5 x \\ \text { d) } \cos 2 x=-\cos 6 x ; & \text { f) } \operatorname{ctg} 2 x=\operatorname{ctg} x\end{array} \)
Trigonometría Romania Mar 12, 2025
prove the following identities: \( \begin{array}{ll}\text { (1) } \cos x \sin x+\sin ^{2} x \tan x=\tan x & \text { (2) } \frac{\tan A \cdot \sin 2 A}{1-\cos A}=2+2 \cos A \\ \text { (3) } \frac{\cos \alpha+\sin \alpha}{\cos 2 \alpha}=\frac{\cos ^{2} \alpha+\sin ^{2} \alpha}{\cos \alpha-\sin \alpha} & \text { (4) } \frac{\sin 2 x-2 \sin x}{\cos 2 x-1}=\frac{1}{\sin x}-\frac{1}{\tan x} \\ \text { (5) } \frac{\sin \theta-\sin 2 \theta}{\cos \theta-\cos 2 \theta-1}=\tan \theta & \text { (6) } \frac{\cos 2 \alpha+\cos \alpha}{\sin 2 \alpha-\sin \alpha}=\frac{\cos \alpha+1}{\sin \alpha}\end{array} \)
Trigonometría South Africa Mar 12, 2025
\( \cos 2 x+\cos x-2=0 \quad \) Genceal Solurion
Trigonometría South Africa Mar 12, 2025

Latest Trigonometry Questions

6. Rezolvaṭi următoarele ecuatii trigonometrice elementare: \( \begin{array}{ll}\text { a) } \sin 5 x=\sin 3 x ; & \text { b) } \cos x=\cos 4 x \\ \text { c) } \cos 5 x=-\sin 3 x ; & \text { d) } \operatorname{tg} 4 x=\operatorname{ctg}\left(3 x+\frac{\pi}{4}\right) ; \\ \begin{array}{ll}\text { e) } \sin \left(\frac{3 \pi}{2}+x\right)+\cos 3 x=0 ; & \text { f) } \cos \left(\frac{3 x}{2}+\frac{\pi}{4}\right)+\sin \left(\frac{2 x}{3}-\frac{\pi}{4}\right)=0\end{array} \\ \text { 7. Rezolvați următoarele ecuații trigonometrice elementare: } \\ \begin{array}{lll}\text { a) } \sin x=\sin 7 x ; & \text { b) }-\sin 2 x=\sin x ; & \text { e) } \operatorname{tg} 4 x=\operatorname{tg} 2 x ;\end{array} & \text { c) } \cos 4 x=\cos 5 x \\ \text { d) } \cos 2 x=-\cos 6 x ; & \text { f) } \operatorname{ctg} 2 x=\operatorname{ctg} x\end{array} \)
Trigonometría Romania Mar 12, 2025
STION 6 Without using a calculator, simplify the following expression to a single trigonometric term: \( \frac{\sin 10^{\circ}}{\cos 440^{\circ}}+\tan \left(360^{\circ}-\theta\right) \cdot \sin 2 \theta \) Given: \( \sin \left(60^{\circ}+2 x\right)+\sin \left(60^{\circ}-2 x\right) \) 6.2 .1 \( 6.2 .2 \quad \) Calculate the value of \( k \) if \( \sin \left(60^{\circ}+2 x\right)+\sin \left(60^{\circ}-2 x\right)=k \cos 2 x \). If \( \cos x=\sqrt{t} \), without using a calculator, determine the value of \( \tan 60^{\circ}\left[\sin \left(60^{\circ}+2 x\right)+\sin \left(60^{\circ}-2 x\right)\right] \) in terms of \( t \).
Trigonometría South Africa Mar 12, 2025
мданыз: \( \frac{\sin (2 \pi-\alpha)}{\operatorname{ctg}\left(\frac{\pi}{2}-\alpha\right)} \cdot \frac{\operatorname{tg}\left(\frac{\pi}{2}+\alpha\right)}{\cos \left(\frac{\pi}{2}+\alpha\right)}+\frac{\cos (2 \pi+\alpha)}{\sin \left(\frac{3 \pi}{2}+\alpha\right)} \)
Trigonometría Kazakhstan Mar 12, 2025
prove the following identities: \( \begin{array}{ll}\text { (1) } \cos x \sin x+\sin ^{2} x \tan x=\tan x & \text { (2) } \frac{\tan A \cdot \sin 2 A}{1-\cos A}=2+2 \cos A \\ \text { (3) } \frac{\cos \alpha+\sin \alpha}{\cos 2 \alpha}=\frac{\cos ^{2} \alpha+\sin ^{2} \alpha}{\cos \alpha-\sin \alpha} & \text { (4) } \frac{\sin 2 x-2 \sin x}{\cos 2 x-1}=\frac{1}{\sin x}-\frac{1}{\tan x} \\ \text { (5) } \frac{\sin \theta-\sin 2 \theta}{\cos \theta-\cos 2 \theta-1}=\tan \theta & \text { (6) } \frac{\cos 2 \alpha+\cos \alpha}{\sin 2 \alpha-\sin \alpha}=\frac{\cos \alpha+1}{\sin \alpha}\end{array} \)
Trigonometría South Africa Mar 12, 2025
\( { }^{\circ} \cos 50^{\circ}+\sin 80^{\circ} \sin 50^{\circ} \) даныз: \( \left(\frac{\sin \alpha}{1+\cos \alpha}+\frac{\sin \alpha}{1-\cos \alpha}\right) \cdot \sin 2 \alpha \) \( \frac{\cos \left(\frac{2 \pi+\alpha)}{3 \pi+\alpha)}\right.}{\left.\frac{3 \pi}{\pi}+\alpha\right)} \)
Trigonometría Kazakhstan Mar 12, 2025
Anterior Próximo
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde Hazte Premium
Estudiar puede ser una verdadera lucha
¿Por qué no estudiarlo en UpStudy?
Seleccione su plan a continuación
Prima

Puedes disfrutar

Empieza ahora
  • Explicaciones paso a paso
  • Tutores expertos en vivo 24/7
  • Número ilimitado de preguntas
  • Sin interrupciones
  • Acceso completo a Respuesta y Solución
  • Acceso completo al chat de PDF, al chat de UpStudy y al chat de navegación
Básico

Totalmente gratis pero limitado

  • Solución limitada
Bienvenido a ¡Estudia ahora!
Inicie sesión para continuar con el recorrido de Thoth AI Chat
Continuar con correo electrónico
O continuar con
Al hacer clic en "Iniciar sesión", acepta nuestros términos y condiciones. Términos de Uso & Política de privacidad