Question

prove tanx + cotx=under root sec^2x+cosec^2x

Answer 1

RHS= under root (1+tan^2x)+(1+cot^2x)
=under root 2+tan^2x+cot^2x
since cotx*tanx=1
thus it is similar to (a+b)^2
therefore----------under root (tanx+cotx)^2
=tanx +cotx
=LHS

Hope this helps!

Answer 2

Hey dear !!!

From given RHS

√sec²²x -cosec²x

•°• sec²x = 1 + tan²x
And , cosec²x = 1 + cot²x

√1+tan²x + 1 + cot²x

√tan²x + cot²x

√tan²x +cot²x + 2×tanx×cotx
{•°• tanx×cotx = 1}

Hence it is in the form of
(a+ b)² = a² + b² + 2ab

Hence ,

√(tanx + cotx)²

= tanx + cotx LHS prooved

******************************
Hope it helps you !!!

@Rajukumar111