If $\sec heta - an heta = m$, then the value of $\sec heta + an heta$ is :

Question

If $\sec	heta - 	an	heta = m$, then the value of $\sec	heta + 	an	heta$ is :

Accepted Answer

## Model Answer **(c) $\dfrac{1}{m}$** Since $\sec^2	heta - 	an^2	heta = 1$, we have $(\sec	heta - 	an	heta)(\sec	heta + 	an	heta) = 1$, so $\sec	heta + 	an	heta = \dfrac{1}{m}$. ## Explanation Use the identity $\sec^2	heta - 	an^2	heta = 1$, which factors as $(\sec	heta - 	an	heta)(\sec	heta + 	an	heta) = 1$. Since $\sec	heta - 	an	heta = m$, dividing both sides by $m$ gives the answer directly.

Mathematics — CBSE Class 10 board question