Question

If 13sinA=5 evaluate 5 sinA -2 cosA/tanA

Answer 1

Explanation:

We have

`\sin A=(5)/(13)`

Draw a right triangle where the side in front of the angle A is 5 and the hypothenuse is 13. Hence the length of the other angle is
`√(13^2-5^2)=12`.

It follows that

`\cos A=(12)/(13)` and
`\tan A= (5)/(12).`

Subtitute this we obtain

`5\sin A-(2\cos A)/(\tan A)=5\cdot (5)/(13)-(12/13)/(5/12)`

which is equal to

`(25)/(13)-(144)/(65)=(125-144)/(165)=-(19)/(165).`