First slide

Trigonometric Identities

Question

$For any real θ the max value of \cos^{2} (\cos θ) + \sin^{2} (\sin θ) =$

Difficult

A

$1 + \sin^{2} 1$
B

$1 + \cos^{2} 1$
C

1
D

2

Solution

$\begin{array}{l} L e t f (θ) = \cos^{2} (\cos θ) + \sin^{2} (\sin θ) \\ W e h a v e - 1 \leq \cos θ \leq 1 and - 1 \leq \sin θ \leq 1 \\ ∴ \cos^{2} 1 \leq \cos^{2} (\cos θ) \leq 1 and 0 \leq \sin^{2} (\sin θ) \leq \sin^{2} 1 \end{array}$
$Max value of f (θ) = 1 + \sin^{2} 1$

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