Question

9. Prove that, (1 - Cos? A) cosec? A= 1.​

Answer 1

Explanation:

We need to prove

1+cosA

1−cosA

=cosecA−cotA

By taking L.H.S. =

1+cosA

1−cosA

=

1+cosA

1−cosA

×

1−cosA

1−cosA

=

1−cos

2

A

(1−cosA)

2

=

sin

2

A

(1−cosA)

2

=

sinA

1−cosA

=

sinA

1

−

sinA

cosA

=cosecA−cotA= R.H.S.

Hence, proved

Answer 2

Answer:

We need to prove

1+cosA

1−cosA

=cosecA−cotA

By taking L.H.S. =

1+cosA

1−cosA

=

1+cosA

1−cosA

×

1−cosA

1−cosA

=

1−cos

2

A

(1−cosA)

2

=

sin

2

A

(1−cosA)

2

=

sinA

1−cosA

=

sinA

1

−

sinA

cosA

=cosecA−cotA= R.H.S.

Hence, proved