Question

Question #fb189

Answer 1

See explanation

Explanation:

We want to verify the identity

`1/(tan(a)+cot(a))=cos(a)sin(a)`

Use the following identities and definitions

• `sin^2(a)+cos^2(a)=1`
• `tan(a)=sin(a)/cos(a)`
• `cot(a)=cos(a)/sin(a)`

`LHS=1/(tan(a)+cot(a))`

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

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

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

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

`=cos(a)sin(a)=RHS`