Question

Prove that 1/1+cosA+1/1-cosA=2cosec^2A

Answer 1

Answer:

To prove:

1/1+cosA + 1/1-cosA = 2cosec²A

Proof:

L. H. S = 1/1+cosA + 1/1-cosA

=1-cosA+1+cosA/1-cos²A

=2/1-cos²A

=2/sin²A

=2cosec²A = R. H. S

Hence L. H. S = R. H. S

Answer 2

To prove: 1/1+CosA +1/1-cosA = 2cosec²A

Step-by-step explanation:

L.H.S...

(1/1+CosA) + (1/1-cosA)

Lcm=1-cos²A [property used.. (a+b) (a-b) =(a²-b²)]

{(1-cosA)+(1+cosA)} / 1-cos²A

Cos A in the numerator gets cancelled.

2/1-cos²A [1-cos²A =sinA]

2/sinA [cosec A=1/sinA]

2 cosecA

L.H.S=R.H.S

HENCE PROVED