Question

show that cos7A/secA - sin7A/cosecA = COS8A

Answer 1

In this question we have to put only just a formula. the formulas are very important

Answer 2

Answer and Explanation:

To show : $\frac{\cos 7A}{\sec A}-\frac{\sin 7A}{\csc A}=\cos 8A$

Solution :

Take LHS,

$LHS=\frac{\cos 7A}{\sec A}-\frac{\sin 7A}{\csc A}$

Write, $\frac{1}{\sec A}=\cos A$ and $\frac{1}{csc A}=\sin A$

$LHS=\cos 7A\times \cos A-\sin 7A\times \sin A$

Using identity, $\cos A\cos B-\sin A\sin B=\cos (A+B)$

Here, A=7A and B = A

$LHS=\cos (7A+A)$

$LHS=\cos (8A)$

$LHS=RHS$

Hence proved.