Question

(C) Prove the identity:
(sec + cosec ) (sin theta + cos theta ) = 2 + sec theta.cosec theta)​

Answer 1

To prove:

(sinθ+cosecθ)

2

+(cosθ+secθ)

2

=7+tan

2

θ+cot

2

θ

Solution:

L.H.S. =(sinθ+cosecθ)

2

+(cosθ+secθ)

2

=sin

2

θ+cosec

2

θ+2sinθ.cosecθ+cos

2

θ+sec

2

θ+2cosθ.secθ

=(sin

2

θ+cos

2

θ)+1+cot

2

θ+2+1+tan

2

θ+2

=1+6+tan

2

θ+cot

2

θ

=7+tan

2

θ+cot

2

θ

= R.H.S.