Question

find whether $\frac{\cos Q-\sin Q+1}{\cos Q+\sin Q+1}=\frac{1-\cos Q}{\sin Q}$ is true or false?

• A. True
• B. False

Answer 1

The correct option is B False

LHS

$\frac{\cos Q-\sin Q+1}{\cos Q+\sin Q+1}$

Dividing Numerator and denominator by $\cos Q$

$⟹\frac{1-\tan Q+\sec Q}{1+\tan Q+\sec Q}$

$⟹\frac{({\sec }^{2}Q-{\tan }^{2}Q)-\tan Q+\sec Q}{1+\tan Q+\sec Q}$

$⟹\frac{(\sec Q+\tan Q)(\sec Q-\tan Q)-\tan Q+\sec Q}{1+\tan Q+\sec Q}$

$⟹\frac{(\sec Q+\tan Q)(1+\tan Q+\sec Q)}{1+\tan Q+\sec Q}$

$⟹\sec Q+\tan Q$

$⟹\frac{1+\cos Q}{\sin Q}$

LHS $\ne$ RHS