Respuesta :

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[tex]\sin x+\cot x\cos x=\sin x+\dfrac{\cos x}{\sin x}\cos x=\dfrac1{\sin x}(\sin^2x+\cos^2x)=\csc x[/tex]
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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.


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