Question

Prove that cos a a divided by 1 minus tan a Plus sin square A / Sin A minus Cos A is equals to sec a + Cos A

Answer 1

Answer:i think rhs should be sina + cos a

Step-by-step explanation:

Answer 2

Answer:

$\frac{\tan A-\sin A}{\sin^2 A}=\frac{\tan A}{1+\cos A}$ hence proved.

Step-by-step explanation:

To prove : $\frac{\tan A-\sin A}{\sin^2 A}=\frac{\tan A}{1+\cos A}$

Proof :

Taking LHS,

$LHS=\frac{\tan A-\sin A}{\sin^2 A}$

$LHS=\frac{\frac{\sin A}{\cos A}-\sin A}{1-\cos^2 A}$

$LHS=\frac{\frac{\sin A-\sin A\cos A}{\cos A}}{1-\cos^2 A}$

$LHS=\frac{\sin A(1-\cos A)}{\cos A(1+\cos A)(1-\cos A)}$

$LHS=\frac{\sin A}{\cos A(1+\cos A)}$

$LHS=\frac{\frac{\sin A}{\cos A}}{\frac{\cos A(1+\cos A)}{\cos A}}$

$LHS=\frac{\tan A}{1+\cos A}$

$LHS=RHS$

Hence proved.

#Learn more