Question

prove the following
( 1 + tanA . tanB )² + ( tanA - tanB )² = sec²A . sec² B​

Answer 1

(tanA−tanB)

2

+(1+tanAtanB)

2

=tan

2

A+tan

2

B−2tanAtanB+1+tan

2

Atan

2

B+2tanAtanB

=tan

2

A+tan

2

B+1+tan

2

(A)tan

2

(B)

=tan

2

(A)[1+tan

2

(B)]+[1+tan

2

(B)]

=(1+tan

2

(B))(1+tan

2

(A))

=sec

2

B.sec

2

A