68. \( \frac{1-\cos x}{\operatorname{sen} x}+\frac{\operatorname{sen} x}{1-\cos x}=2 \csc x \) 66. \( \frac{\csc x-\cot x}{\sec x-1}=\cot x \) 67. \( \tan ^{2} a-\operatorname{sen}^{2} a=\tan ^{2} u \operatorname{sen}^{2} a \) 68. \( \sec ^{4} x-\tan ^{4} x=\sec ^{2} x+\tan ^{2} x \) 69. \( \frac{1+\tan x}{1-\tan x}=\frac{\cos x+\operatorname{sen} x}{\cos x-\operatorname{sen} x} \) 70. \( \frac{\cos \theta}{1-\operatorname{sen} \theta}=\frac{\operatorname{sen} \theta-\csc \theta}{\cos \theta-\cot \theta} \) 71. \( \frac{1}{\sec x+\tan ^{x}}+\frac{1}{\sec x-\tan x}=2 \sec x \) 72. \( \frac{\cos t+\tan ^{2} t-1}{\operatorname{sen}^{2} t}=\operatorname{tin}^{2} t \)

2.4 Prove that: \[ \begin{array}{l}\frac{1}{1+\cot ^{2} x}+\frac{1}{1+\tan ^{2} x}=1 \\ 2.5 \text { Solve for } x \text { for } x \in\left[0^{\circ} ; 360^{\circ}\right], \text { correct to ONE decimal digit: } \\ -\frac{2}{3} \sin x+0,524=0\end{array} \]

Sea \( f(x)=7 \cos \left(x+\frac{\pi}{2}\right)+3 \). Entonces el mínimo valor que puede alcanzar \( f(x) \) es

2.1 If \( \hat{\mathrm{A}}=310^{\circ} \) and \( \hat{\mathrm{B}}=130,5^{\circ} \), determine the following values, correct to ONE decimal digit: \( 2.1 .1 \quad \tan 3 B+\frac{1}{3} \cos \frac{A}{3} \) \( 2.1 .2 \quad-\sec \left(\frac{A}{4}-2 B\right) \) 2.2 If \( \cot \theta=-\frac{12}{5} \) and \( \sin \theta>0 \), determine the value of \( 20 \operatorname{cosec} \theta-12 \sec \theta \), WITHOUT the use of a calculator. 2.3 Simplify the following expression: \( \frac{\sin \left(360^{\circ}-x\right) \sec \left(180^{\circ}+x\right)}{\tan \left(180^{\circ}-x\right) \operatorname{cosec}\left(360^{\circ}+x\right)} \)

You are given that \( \cos (A)=-\frac{3}{5} \), with \( A \) in Quadrant \( I I \), and \( \cos (B)=\frac{8}{17} \), with \( B \) in Quadrant \( I \). Find \( \cos (A-B) \). Give your answer as a fraction. Sorry, that's incorrect. Try again?

usa el tecrema del seno para encontrar el angulo opuesto al lado mas pequeño en untriangulo dondé \( a=7, b=10 \), y el angulo opuesto a b es \( 40^{\circ} \)