Question

prove : (cos theta /1-tan theta)- (sin^2theta /cos theta - sin theta) = cos theta +sin theta​

Answer 1

Answer:

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Answer 2

Answer:

Step-by-step explanation:

Cos θ/ 1-Tanθ = Cos θ/ (Cos θ - sin θ/ Cos θ)

                        = Cos² θ/ Cos θ - Sin θ

Given,

Cos θ/ 1-Tanθ - Sin²θ/ Cos θ- Sinθ =  

                            = Cos² θ/( Cos θ - Sin θ) - Sin²θ/ Cos θ- Sinθ

                            = Cos² θ -  Sin²θ/Cos θ - Sin θ

                            = (Cos θ - Sin θ)(Cos θ + Sin θ) / (Cos θ - Sin θ)

                            = (Cos θ + Sin θ)

Because a² - b²= (a+b)(a-b)