Question

Proove that
cosec A + 2 cosec 2A = sec A cot (A/2)
please answer fast i will mark it as brainliest if correct ​

Answer 1

Question :

Proove that cosec A + 2 cosec 2A = sec A cot (A/2)

Solution :

$\sf \small cosec \: A + 2 cosec \:2 A = sec \: A \: cot \frac{A}{2}$

$\sf \small \frac{1}{sin \: A} + \frac{2}{sin \: 2A} = \frac{1}{sin \: A} + \frac{2}{2 \: sin \: A \: cos \: A}$

$\sf \frac{cos \:A + 1 }{sin \: A \: cos \:A } = \frac{2 \: {cos}^{2} \: \frac{A}{2} }{2 \: sin \: \frac{A}{2} \: cos \: \frac{A}{2} cos \: A}$

$\sf \small \: cosec \: A + 2 \: cosec \: 2 \: A = sec \: A \: cot \: A$

HENCE PROVED ✓✓

Answer 2

Answer:

L.H.S. =sec

2

A+cosec

2

A

⇒

cos

2

A

1

+

sin

2

A

1

⇒

sin

2

Acos

2

A

sin

2

A+cos

2

A

⇒

sin

2

Acos

2

A

1

⇒cosec

2

Asec

2

A= R.H.S.