First slide

Trigonometric equations

Question

If $0 < x < π / 2 and \sin (2 \sin x) = \cos (2 \cos x)$ then $\tan x + \cot x = \frac{a}{π^{C} - b} where a + b + c =$

Moderate

A

32
B

16
C

50
D

64

Solution

$\begin{array}{l} \sin (2 \sin x) = \sin (π / 2 - 2 \cos x) \\ \Rightarrow 2 \sin x = π / 2 - 2 \cos x \\ \Rightarrow \sin x + \cos x = π / 4 \\ \Rightarrow 1 + \sin 2 x = π^{2} / 16 \end{array}$
$\begin{array}{l} \tan x + \cot x = \frac{2}{\sin 2 x} = \frac{32}{π^{2} - 16} \\ a = 32, b = 16, c = 2 \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App