Question

Prove that : (sec A sec B + tan A tan B )2
- (sec A tan B + tan A sec B )2 = 1​

Answer 1

Step-by-step explanation:

Given secAtanB+tanAsecB=91

Squaring both sides, we get

⇒sec

2

Atan

2

B+tan

2

Asec

2

B+2tanAtanBsecAsecB=8281

⇒2tanAtanBsecAsecB=8281−sec

2

Atan

2

B−tan

2

Asec

2

B ...(1)

Consider, (secAsecB+tanAtanB)

2

=sec

2

Asec

2

B+tan

2

Atan

2

B+2tanAtanBsecAsecB

=sec

2

Asec

2

B+tan

2

Atan

2

B+8281−sec

2

Atan

2

B−tan

2

Asec

2

B (by (1))

=sec

2

A−tan

2

A+8281

=8282