Question #029c3

1 Answer
Oct 2, 2017

Proved 1/[cos x(1+cos x)]= [tan x -sin x]/sin^3x

Explanation:

Given, 1/[cos x(1+cos x)] = [tan x - sin x]/sin^3x

We have to prove either way. Let me take Left Hand Side (L.H.S.)

1/[cos x (1+cos x)]

rArr [1.(1-cos x)]/[cos x (1+cos x)(1-cos x) [ multiply both sides by (1 - cos x)]

rArr [1 - cos x]/[cos x (1 - cos^2 x)]

rArr [(1-cos x)/cos x]/sin^2x [ as sin^2x + cos^2x = 1. so, 1-cos^2x = sin^2x]

rArr [1/cos x - cos x/cos x]/sin^2x

rArr [(1/cos x -1)sin x]/[sin^2 x. sin x] [ multiply both sides by sin x]

rArr [sin x/cos x - sin x]/sin^3x

rArr (tan x - sin x)/sin^3x = R. H. S.