Question

Math toppers answer the questions........
correct answer will be marked as brainlist​

Answer 1

1) cos θ/(1 - tan θ) + sin θ/(1 - cot θ) = sin θ + cos θ

Solution:

L.H.S = cos θ/(1 - tan θ) + sin θ/(1 - cot θ)

= cos θ/{1 - (sin θ/cos θ)} + sin θ/{1 - (cos θ/sin θ)}

= cos θ/{(cos θ - sin θ)/cos θ} + sin θ/{(sin θ - cos θ/sin θ)}

= cos2 θ/(cos θ - sin θ) + sin2 θ/(cos θ - sin θ)

= (cos2 θ - sin2 θ)/(cos θ - sin θ)

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

= (cos θ + sin θ) = R.H.S. Proved.