Question

1/(sec(theta) - 1) + 1/(sec(theta) + 1) = 2cot theta cosectheta​

Answer 1

Answer:

See the step by step explanation

Step-by-step explanation:

LHS

$=\frac{1}{\sec \theta-1}+\frac{1}{\sec \theta+1}=\frac{\sec \theta+1+\sec\theta-1}{(\sec \theta-1)(\sec\theta+1)}$

$=\frac{2\sec\theta}{\sec^2\theta-1}=\frac{2\sec\theta}{\tan^2\theta}$, since $\sec^2 \theta-\tan^2\theta=1$

$=\frac{\frac{2}{\cos\theta}}{\frac{\sin^2\theta}{\cos^2\theta}}=\frac{2}{\cos\theta}\times \frac{\cos^2\theta}{\sin^2\theta}=2\times \frac{1}{\sin\theta}\times \frac{\cos\theta}{\sin\theta}=2\cos ec\theta\cot\theta=$RHS