Question

sinA/(1+ cosA) = cosecA - cotA prove​

Answer 1

Answer:

Answer and Explanation:

To prove : \frac{\sin A}{1+\cos A}=\csc A-\cot A

1+cosA

sinA

=cscA−cotA

Proof :

Taking LHS,

\frac{\sin A}{1+\cos A}

1+cosA

sinA

Rationalize,

=\frac{\sin A}{1+\cos A}\times \frac{1-\cos A}{1-\cos A}=

1+cosA

sinA

×

1−cosA

1−cosA

=\frac{\sin A(1-\cos A)}{(1+\cos A)(1-\cos A)}=

(1+cosA)(1−cosA)

sinA(1−cosA)

=\frac{\sin A(1-\cos A)}{1^2-\cos^2 A}=

1

2

−cos

2

A

sinA(1−cosA)

=\frac{\sin A(1-\cos A)}{\sin^2 A}=

sin

2

A

sinA(1−cosA)

=\frac{1-\cos A}{\sin A}=

sinA

1−cosA

=\frac{1}{\sin A}-\frac{\cos A}{\sin A}=

sinA

1

−

sinA

cosA

=\csc A-\tan A=cscA−tanA

= RHS

So, LHS=RHS hence proved