Question

Prove that tan(a+b)+tan(a-b)=si 2a/cos^2a-sin^2b

Answer 1

Step-by-step explanation:

tan(A+B)-tan(A-B)

=(tanA+tanB/1-tanAtanB)- (tanA-tanB/1+tanAtanB)

=(tanA+tanB)(1+tanAtanB)-(tanA-tanB) (1-tanAtanB)/1-tan²Atan²B

=2tanB+2tan²AtanB/1-tan²Atan²B

=(2tanB+2tan²AtanB)(cos²Acos²B)/ (1-tan²Atan²B)(cos²Acos²B)

=2sinBcos²AcosB+2sin²AsinBcosB/ cos²Acos²B-sin²Asin²B

=2sinBcosB(cos²A+sin²A)/ cos²A(1-sin²A)-sin²B(1-cos²A)

=sin2B/cos²A-cos²Asin²A-sin²B+sin²Bcos²A

=sin2B/cos²A-sin²B