Question

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Hey please help me in solving this trigonometry identities question.

Please write with the steps so that I can understand.

Best answer will be the brainliest

Thank you ^_^

Answer 1

hope it will help you

Answer 2

(1 + tanAtanB)² + (tanA - tanB)² = sec²Asec²B

LHS

=1 + tan²Atan²B +2tanAtanB + tan²A + tan²B - 2tanAtanB

------------------[ (a + b)² = a² + b² +2ab and (a - b)²= a² + b² -2ab]

=1 + tan²Atan²B +tan²A + tan²B

=1 +tan²A + tan²B(tan²A +1 )

=sec²A + tan²Bsec²A -------------------[ 1 +tan²x = sec²x}

=sec²A(1 + tan²B)

=sec²Asec²B

LHS=RHS

Hence Proved.