Question

$\sqrt{1 + cosa \frac{ \sqrt{1 + cos a} } = cosec a + cot a$
​

Answer 1

Answer:

Prove:

1+cos A

1−cos A

=cosec A−cot A

ANSWER

1+cosθ

1−cosθ

=cosecθ−cotθ

L.H.S Rationalizing,

1−cos

2

θ

(1−cosθ)

2

=

1−cos

2

θ

1−cosθ

=

sin

2

θ

1−cosθ

=

sinθ

1−cosθ

=

sinθ

1

−

sinθ

cosθ

=cosesθ−cotθ

=R.H.S

∴ L.H.S=R.H.S

Hence proved.