Evaluate the following: 70^ cosec 20^ + 59^ 31^ - Vidyadip

Question

Evaluate the following:
$\frac{\sec70^\circ}{\text{cosec }20^\circ}+\frac{\sin59^\circ}{\cos31^\circ}$

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Answer

We have to find: $\frac{\sec70^\circ}{\text{cosec }20^\circ}+\frac{\sin59^\circ}{\cos31^\circ}$$$ Since $\frac{\sec70^\circ}{\text{cosec }20^\circ}+\frac{\sin59^\circ}{\cos31^\circ}$ and $\sec(90^\circ-\theta)=\text{cosec }\theta$ So, $\frac{\sec70^\circ}{\text{cosec }20^\circ}+\frac{\sin59^\circ}{\cos31^\circ}=\frac{\sec(90^\circ-20^\circ)}{\text{cosec 20}^\circ}+\frac{\sin(90^\circ-31^\circ)}{\cos31^\circ}$ $=\frac{\text{cosec }20^\circ}{\text{cosec }20^\circ}+\frac{\cos31^\circ}{\cos31^\circ}$ $= 1 + 1$ $= 2$value of $\frac{\sec70^\circ}{\text{cosec }20^\circ}+\frac{\sin59^\circ}{\cos31^\circ}\text{ is 2}$

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