` (cos 7x - cos3x)/(sin7x-2 sin5x+sin3x)` किसके बराबर है ?

Options

A. `tan x`
B. `cotx`
C. `tan 2x`
D. ` cot 2x`

Answer

b

Explanation

` (cos 7x-cos3x)/(sin7x-2sin 5x+sin3x)`
` (-2 sin.((7x+3x)/2) *sin. ((7x-3x)/2))/(2sin. ((7x+3x)/2)* cos((7x-3x)/2)-2 sin 5x)`
` [ cos C - cos D "तथा " sin C + sin D सूत्र से ]`
` (-2sin 5x* sin 2x)/(2sin 5x*cos 2x-2sin 5x)`
` = (-2 sin 5x*sin 2x)/(-2 sin 5x (-cos 2x+1))`
` = (sin 2x)/((1-cos 2x))`
` = (sin2x)/(1-(1-2sin^(2)x))[:' cos 2 x = 1 - 2 sin^(2)x]`
` (sin 2x)/(1-1+2sin^(2)x)= (2sinx*cosx)/(2sin^(2)x)`
` = (cosx)/(sinx) = cotx`