Question

prove that sin theta/1-cot theta+cos theta/1-tan theta =sin theta+cos theta​

Answer 1

Answer:

cos θ + sin θ

Solution:

[sin θ/(1 – cot θ)] + [cos θ/(1 – tan θ)]

= [sin2θ/(sin θ – cos θ)] + [cos2θ/(cos θ – sin θ)] {since cot θ = cos θ/sin θ and tan θ = sin θ/cos θ}

= [sin2θ(sin θ – cos θ)] – [cos2θ(sin θ – cos θ)]

= (sin2θ – cos2θ)/(sin θ – cos θ)

= [(sin θ + cos θ)(sin θ – cos θ)]/ (sin θ – cos θ)

= sin θ + cos θ

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

hope this helps...

Substituting tanø and cotø by sinø/cosø and cosø/sinø respectively and using the algebraic identity (a²-b²)=(a+b)(a-b)