Evaluate the following: 50^ 40^ + 40^ 50^ - Vidyadip

Question

Evaluate the following:
$\sec50^\circ\sin40^\circ+\cos40^\circ\text{cosec }50^\circ$

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Answer

We have to find $\sec50^\circ\sin40^\circ+\cos40^\circ\text{cosec }50^\circ$
Since $\cos(90^\circ-\theta)=\sin\theta,\sec(90^\circ-\theta)=\text{cosec }\theta$ and $\sin\theta.\text{cosec }\theta=1$
So, $\sec50^\circ\sin40^\circ+\cos40^\circ\text{cosec }50^\circ$
$=\sec(90^\circ-40^\circ)\sin40^\circ+\cos(90^\circ-50^\circ)\text{cosec }50^\circ$
$=1+1$
$=2$
So value of $\sec50^\circ\sin40^\circ+\cos40^\circ\text{cosec }50^\circ\text{ is }2$

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