Question

If 13 sin θ=12 cos θ, find the value

Answer 1

From the given information, we have

`13\sin(\theta) = 12\cos(\theta) \implies (\sin(\theta))/(\cos(\theta)) = (12)/(13)`

In the expression of interest, divide through everything by
`\cos^2(\theta)` to get

`(2\sin(\theta)\cos(\theta))/(\cos^2(\theta) - \sin^2(\theta)) = (2(\sin(\theta))/(\cos(\theta)))/(1 - (\sin^2(\theta))/(\cos^2(\theta)))`

Then plugging in the given info, we get

`(2\sin(\theta)\cos(\theta))/(\cos^2(\theta) - \sin^2(\theta)) = (2* (12)/(13))/(1 - \left((12)/(13)\right)^2) = \boxed{(312)/(25)}`