Question

$prove that : \frac{1}{sin 10} -\frac{\sqrt{3} }{cos 10} =4$

Answer 1

to prove

formula to prove this

Sin (A) Cos (B) - Cos (A) Sin(B) = (Sin A-B)

2Sin (A) Cos (A) = Sin (2A)

[tex]\begin{lgathered}\frac{1}{sin(10)} - \frac{ \sqrt{3} }{cos(10)} \\ \\ 4 [ \frac{ \frac{1}{2} cos(10) - \frac{ \sqrt{3} }{2} sin(10) }{2 sin(10) cos(10)} ] \\ \\ 4[ \frac{sin(30) cos(10) - cos(30) sin(10)}{2 sin(10) cos(10)} ] \\ \\ 4[ \frac{sin(20)}{sin(20)} ] \\ \\ 4\end{lgathered}sin(10)1​−cos(10)3​​4[2sin(10)cos(10)21​cos(10)−23​​sin(10)​]4[2sin(10)cos(10)sin(30)cos(10)−cos(30)sin(10)​]4[sin(20)sin(20)​]4​

Answer 2

Answer:

Hey.... here is your answer in the image.

Hope it helps! ! !