Question

solve the question fast

Answer 1

using the three standard identities we first break tan to simpler term of cos and then simplify as shown in above pic

Answer 2

hey there,

Use the identity tanA = sin/cosA
Tan²A - tan²B = sin²A - sin²B/ cos²A cos²B
LHS = tan²A - tan²B
= sin²A/ cos²A - sin²B/ cos²B
= sin²A cos²B - sin²B cos²A/ cos²A cos²B
= sin²A (1 - sin²B) - sin²B (1 - sin²A) / cos²A cos²B
= sin²A - sin²B sin²A - sin²B + sin²B / cos²A cos²B
= sin²A - sin²B / cos²A cos²B = RHS

Hope this helps!