First slide

Trigonometric Identities

Question

$If y = (\sin x + cosec x)^{2} + (\cos x + \sec x)^{2} then min value of y =$

Easy

A

7
B

3
C

9
D

0

Solution

$\begin{array}{l} y = \sin^{2} x + {cosec}^{2} x + 2 + \cos^{2} x + \sec^{2} x + 2 \\ = 5 + \cos e c^{2} x + \sec^{2} x \\ = 5 + 2 + \tan^{2} x + \cot^{2} x \\ = 7 + (\tan x - \cot x)^{2} + 2 \\ \geq 9 \\ y_{\min} = 9 \end{array}$

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