Question

find sin theta/(1-cot theta) + cos theta/(1-tan theta)​

Answer 1

Step-by-step explanation:

4) cos θ + sin θ

Answer: (4) 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