Question

Find dy/dx if y=sin-1 (3sinx+4cosx/5).

Answer 1

$dy/dx = \frac{1}{\sqrt{1-(3Sinx+4cosx/5)^2}}*(3 cosx -4sinx/5)$

Answer 2

Answer:

1

Explanation:

y=sin^-1(3/5.sinx+4/5.cosx)

put 3/5=cosA &4/5=sinA

tanA=4/3

hence A =tan^-1(4/3)

now,

y=sin^-1(cosA.sinx+sinA.cosx)

y=sin^-1[sin(A+x)]

means y=A+x

but A=tan^-1(4/3)

y=tan^-1(4/3)+x

now,

diff.w.r.t.x

dy/dx= 0+1

dy/dx=1