Question

Sin A /1+cos A = cosec A - cot A ?

Answer 1

See explanation

Explanation:

We want to verify the identity

`sin(a)/(1+cos(a))=csc(a)-cot(a)`

We will use

• `sin^2(a)+cos^2(a)=1`

And the basic definitions of trigonometric functions

`LHS=sin(a)/(1+cos(a))`

`=(sin(a)(1-cos(a)))/((1+cos(a))(1-cos(a)))`

`=(sin(a)-sin(a)cos(a))/(1-cos^2(a))`

`=(sin(a)-sin(a)cos(a))/sin^2(a)`

`=sin(a)/sin^2(a)-(sin(a)cos(a))/sin^2(a)`

`=1/sin(a)-cos(a)/sin(a)`

`=csc(a)-cot(a)=RHS`