Question

II
ec A-tan A
Sec A+ tan A
Cos 2B-Cos 2A - Cot (A+B).cot (A-B)
Cos 2B+Cos 2A
Cos 6A-COS 4A
= tan A
Sin 6A +Sin 4A​

Answer 1

Answer:

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)

Step-by-step explanation: