Giving answers to the nearest degree, find in the interval 0<x<360

Giving answers to the nearest degree, find in the interval 0<x<360 all the solutions of:

10 sin(x+26) cos(x+26)=1

rather than the answer, id like to know the solution ie how to work it out.

i have my mock exam tomorrow, please answer me asap please.

thanks,
neilofbodom

Use the identity $\displaystyle \displaystyle \sin{(2\theta)} \equiv 2\sin{(\theta)}\cos{(\theta)}$. If you let $\displaystyle \displaystyle x + 26 = \theta$ then

$\displaystyle \displaystyle 10\sin{(x + 26)}\cos{(x + 26)} \equiv 5\cdot 2\sin{(x + 26)}\cos{(x + 26)} \equiv 5 \sin{[2(x + 26)]}$.

So now you need to solve $\displaystyle \displaystyle 5\sin{[2(x + 26)]} = 1$.

oh ok. so then, ill find what x is and use the general solution of sin to find the other values, right?

Yes. Remember that the sine function is positive in the first and second quadrants.

ok thank you so much!