Question

if 4 cos theta -3 sectheta =2tan theta then theta is

Answer 1

Answer:

here is your answer..........

Answer 2

Answer:

$18^{0}$

Step-by-step explanation:

   4 cos∅ = - 3 sec∅ = 2 tan∅

Let ∅ = x .

=> $4cosx - 3sec x = 2 tanx$

=> $4cosx-\frac{3}{cosx} =2 \frac{sinx}{cosx }$

=> $4cos^{2} x -3 = 2 sinx$

=> $4 - 4sin^{2} x - 3 = 2sinx$

=> $4sin^{2} x +2sinx-1=0$

=> $sinx = \frac{-1 + \sqrt{4+16} }{2*4 }$ or $\frac{-1-\sqrt{4+16} }{2*4 }$

=> $sinx = \frac{\sqrt{5} -1}{4} (or ) \frac{-\sqrt{5}-1 }{4}$

Here, $\frac{-\sqrt{5}-1 }{4}$ is not possible

So, $sinx = \frac{\sqrt{5} -1}{4}= sin18^{0}$

Therefore, x = ∅ = $18^{0}$