Question

The expression sinx + cotx cosx can be simplified to___. A. cotx B. cscx C. cosx sinx D. secx

Answer 1

$\sin x+\cot x\cos x=\sin x+\dfrac{\cos x}{\sin x}\cos x=\dfrac1{\sin x}(\sin^2x+\cos^2x)=\csc x$

Answer 2

Answer:

Solution-

∵ cotx = (cosx÷sinx)

∴ The given expression can be written as

sinx + cotx·cosx = sinx + ( cosx÷ sinx).cosx

⇒sinx +(cosx)²÷sinx = [ (sinx)² + (cosx)²] ÷ sinx

⇒ 1÷ sinx = cosecx = cscx

using the identity (sinx)²+(cosx)²=1

∴ option B is correct.