Question

sin theta+cosec theta/sin theta=2+cot^2 theta​

Answer 1

Step-by-step explanation:

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