Question

Prove that sin θ ( 1 – tan θ ) − cos θ ( 1 − cot θ ) = cosec θ − sec θ

Answer 1

Step-by-step explanation:

sinθ(1+tanθ)+cosθ(1+cotθ)

=sinθ+

cosθ

sin

2

θ

+cosθ+

sinθ

cos

2

θ

=sinθ+

sinθ

cos

2

θ

+

cosθ

sin

2

θ

+cosθ

A=

sinθ

sin

2

θ+cos

2

θ

+

cosθ

sin

2

θ+cos

2

θ

As,sin

2

θ+cos

2

θ=1

A=

sinθ

1

+

cosθ

1

= cosecθ+secθ