Question

If Cot 3x = 4/3, then find the value of 3 cosec x - 4 sec x

Answer 1

The value of 3 cosec x - 4 sec x = 10.

Step-by-step explanation:

1. Here given that

cot 3x = $\frac{4}{3}$.

Then

sin 3x = $\frac{3}{5}$      ...1)

cos 3x =$\frac{4}{5}$.     ...2)

2. 3 cosec x - 4 sec x

 =  $\frac{3}{\sin x}-\frac{4}{\cos x}$

= $\frac{3\cos x-4\sin x}{\sin x\cos x}$

= $5\times (\frac{\frac{3}{5}\cos x-\frac{4}{5}\sin x}{\sin x\cos x})$    ...3)

3. Now from equation 1 and  equation 2 , equation 3 can be written as

= $5\times (\frac{\sin 3x\cos x-\cos 3x\sin x}{\sin x\cos x})$

= $5\times (\frac{\sin (3x-x)}{\sin x\cos x})$

= $5\times (\frac{\sin 2x}{\sin x\cos x})$

= $5\times (\frac{2\sin x\cos x}{\sin x\cos x})$

= 5×2= 10