Question

Prove that (cosecQ-cosQ) ^2=1-cosQ/1+cosQ

Answer 1

Answer:

RHS =

1+cosA

1−cosA

×

1−cosA

1−cosA

=

1−cos

2

A

(1−cos)

2

=

sin

2

A

(cos

2

A−1)

2

LHS =(cotA−cosecA)

2

=(

sinA

cosA

−

sinA

1

)

2

sin

2

A

(cosA−1)

2

= RHS

∴ Hence, proved