Question

Prove that cos -sin+1/cos+sin-1= cosec +cot

Answer 1

Hope it's useful

try it yourself.

Answer 2

given cos-sin+1/cos+sin-1

now rationalising it

(cos-sin)+1*cos+sin+1/(cos+sin)-1*cos+sin)-1

thus we get cos^2-sin^2+cos+sin+cos-sin+1/2cossin+cos^2+sin^2-cos-sin+cos+sin-1

on solving we get

2cos^2/2sincos+2cos/2sincos

cos/sin+1/sin

cot+cosec

HENCE PROVED

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