I have basic knowledge of identities.
Solve each equation for theta if zero degrees is less than or equal to theta is less than or equal to 360 degrees.
1. 4sin theta - 3csc theta = 0
2. sec theta - 2tan theta = 0
(1)4sin theta - 3csc theta = 0 --> 4 sin x - 3 csc x = 0;
4 sin x - 3(1/sin x) = 0,
(4 sin^2 x - 3)/sin x = 0,
4 sin^2 x - 3 = 0,
4 sin^2 x = 3,
sin^2 x - 3/4 = 0, factoring it.
(sin x + (sqrt 3)/2)(sin x - (sqrt 3)/2) = 0, the roots are
sin x = (sqrt 3)/2, -(sqrt 3)/2.
x = arcsin ((sqrt 3)/2, -(sqrt 3)/2)
x = {60, 120, 240, 300 degrees} or {pi/3, 2pi/3, 4pi/3, 5pi/3}
Hello roflcoptur$\displaystyle \sec\theta -2\tan\theta=0$
$\displaystyle \Rightarrow \frac{1}{\cos\theta}-\frac{2\sin\theta}{\cos\theta}=0$
$\displaystyle \Rightarrow \frac{1-2\sin\theta}{\cos\theta}=0$
$\displaystyle \Rightarrow 1-2\sin\theta=0$
$\displaystyle \Rightarrow \sin\theta = \tfrac12$
$\displaystyle \Rightarrow \theta = 30^o, 150^o$
Grandad