Question
1. Simpilfy the following expression as much as possible: \[ \frac{-5 \sin ^{2} A+5}{2 \cos A} \] INSTRUCTION: If you need to type a trigonometric expression, put brackets around the angle. For example: sin(A) or cos(A). Answer: The simplified expression is
Ask by Delgado Murray. in South Africa
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \( \frac{5\cos(A)}{2} \).
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The Deep Dive
The simplified expression is \(-\frac{5(\sin^2(A) - 1)}{2 \cos(A)}\). By applying the Pythagorean identity \(\sin^2(A) + \cos^2(A) = 1\), we can express \(\sin^2(A)\) in terms of \(\cos^2(A)\). In this case, recognizing that \(\sin^2(A) - 1 = -\cos^2(A)\) can help further simplify the expression.