Question

Select the correct answer from each drop-down menu.

(cos2x-cos4x)/(sin2x+sin4x)=

a. cot x

b. tan x

c. sin x

d. cos x


(cos2x+cos4x)/(sin2x-sin4x)=

a. cot x

b. -cot x

c. sin x

d. -tan x

Answer 1

`(b)\\\tan x, \cot x`

Explanation:

Given

trigonometric function is

`(\cos 2x-\cos 4x)/(\sin 2x+\sin 4x)`

Applying trigonometric formulae

`\Rightarrow \cos C-\cos D=-\sin ((C+D)/(2))\sin ((C-D)/(2))\\\\\Rightarrow \sin C+\sin D=\sin ((C+D)/(2))\cos ((C-D)/(2))`

`\Rightarrow (\cos 2x-\cos 4x)/(\sin 2x+\sin 4x)=(2\sin 3x\cdot \sin x)/(2\sin 3x\cdot \cos x)\\\\\Rightarrow (\sin x)/(\cos x)=\tan x`

option (b) is correct

`\Rightarrow (\cos 2x+\cos 4x)/(\sin 2x-\sin 4x)=(2\cos 3x\cdot \cos x)/(2\cos 3x\cdot \sin (-x))=-\cot x`