Question

if sec theta+tan theta = p,than prove that sin theta= p²-1/p²+1​​

Answer 1

Step-by-step explanation:

p

2

−1

=

(secθ+tanθ)

2

+1

(secθ+tanθ)

2

−1

sec

2

θ+tan

2

θ+2secθtanθ+1

sec

2

θ+tan

2

θ+2secθtanθ−1

=

sec

2

θ+(tan

2

θ+1)+2secθtanθ

(sec

2

θ−1)+tan

2

θ+2secθtanθ

=

sec

2

θ+sec

2

θ+2secθtanθ

tan

2

θ+tan

2

θ+2secθtanθ

=

2sec

2

θ+2secθtanθ

2tan

2

θ+2secθtanθ

=

2secθ(secθ+tanθ)

2tanθ(tanθ+secθ)

=

2secθ

2tanθ

=tanθ×cosθ

=

cosθ

sinθ

×cosθ

=sinθ