Question

Prove that tan(A+B)/cot(A-B)=sin^2A-Sin^2B/Cos^2A-Sin^2B

Answer 1

tan (A+B) / cot (A-B)
= tan(A+B) * tan(A-B)
= (tanA+tanB)/(1-tanAtanB) * (tanA-tanB)/(1+tanAtanB)
= (tan^2A - tan^2B)/ (1-tan^2Atan^2B)
= (sin^2A/cos^2A - sin^2B/cos^2B) /[(cos^2Acos^2B - sin^2Asin^2B)/(cos^2Acos^2B)]
= (sin^2A/cos^2A - sin^2B/cos^2B)* (cos^2Acos^2B) / (cos^2Acos^2B -sin^2Asin^2B)
= (sin^2Acos^2B- sin^2Bcos^2A) /(cos^2Acos^2B - sin^2Asin^2B)
= (sin^2A(1-sin^2B) - sin^2B(1-sin^2A)) /[cos^2A(1-sin^2B) - sin^2B(1-cos^2A)]
= (sin^2A-sin^2Asin^2B +sin^2Asin^2B -sin^2B) / (cos^2A-cos^2Asin^2B +cos^2Asin^2B - sin^2B)
= (sin^2A - sin^2B) / (cos^2A - sin^2B)

Answer 2

hiii mate

your answer is in the attachment