Question

Find csc x if sin x + cot x cos x =√3

a. 9
b. 3
c. √(3)/2
d. √(3)

Answer 1

D is the correct answer

Answer 2

`\boxed{d.\:\:\:\csc(x)=√(3)}`

Explanation:

The given trigonometric equation is

`\sin(x)+\cot(x) \cos(x)=√(3)`

Recall that;

`\cot(x)=(\cos(x))/(\sin(x))`

This implies that;

`\sin(x)+(\cos(x))/(\sin(x))* \cos(x)=√(3)`

We collect LCM for the denominator on the left hand side to obtain;

`(\sin^2(x)+\cos^2(x))/(\sin(x))=√(3)`

Recall that;

`sin^2x+cos^2x=1`

`(1)/(\sin(x))=√(3)`

Recall again that;

`(1)/(sinx)=cscx`

`\Rightarrow \csc(x)=√(3)`