Simplify the trigonometric expression sin3 times sin x cos2

Simplify the trigonometric expression. sin^3 times + sin x cos^2 x Simplify the trigonometric expression. csc x + 1/cot x + cos x

sin³x + sinx cos²x

taking sinx out from them

=sinx(sin²x + cos²x)

=sinx * 1 ( Since sin²x +cos²x=1)

= sin x

Therefore sin³x + sinx cos²x = sin x

11. (cscx + 1)/(cotx + cosx)

cscx=1/sinx and cotx=cosx/sinx

=(1/sinx +1)/(cosx/sinx + cos x)

= (1+sinx)/sinx/(cosx+sinx cosx)/sinx

= (1+sinx)/cosx(1+sinx)

= 1/cosx

=secx

(cscx+1/(cotx + cosx))= secx