Question

Calculus :

Inverse functions:

Prove that:

sin( x+ tan^-1(cotx)) = 1

Answer 1

its more a trigo prob than calculus..

u can use the eqn cot(x) = tan(pi/2 - x) to simplify tan-1(cot(x))

Answer 2

I found another solution , by assuming that tan inverse of cotx = y
tany = cotx , drawing the triangle and

sin(x + y) = sinx cos y + siny cos x = sin^2x + cos^2y ( from the triangle) = 1

But I am interested in knowing , how you would solve it.

Answer 3

mine would be tan-1(cotx)=tan-1(tan(pi/2-x))=pi/2 - x

the rest would follow but ur way works just fine too :)

Answer 4

Ok, I got it sin(x + tan^-1 tan(90 - x)) = 90

Answer 5

Correct!

Answer 6

I believe , your method is way better.

Answer 7

Both works :)

Answer 8

Thanks.