Question

Please help
Trigonometric identities proof

(cot^2(x)(sec(x)-1))/1+sin(x)=(sec^2(1-sin(x))/1+sec(x)

Many Thanks

Answer 1

you need to learn to use parentheses online to make it clear what you want, since otherwise, multiplication gets done before addition. You meant

(cot^2(x)(sec(x)-1))/(1+sin(x))=(sec^2(1-sin(x))/(1+sec(x))

Apply some of your elementary identities:

cot^2(sec-1) = (sec-1)/tan^2
= (sec-1)/(sec^2-1)
= (sec-1)/((sec-1)(sec+1))
= 1/(sec+1)

That should get you started...