Evaluate: = 50^ 40^ + cosec 40^ 50^ -4 50^ cosec 40^ - Vidyadip

Question

Evaluate:
$=\frac{\sin50^\circ}{\cos40^\circ}+\frac{\text{cosec }40^\circ}{\sec50^\circ}-4 \cos50^\circ\ \text{cosec }40^\circ$

✓

Answer

We will use the properties of complementary angles.
$=\frac{\sin50^\circ}{\cos40^\circ}+\frac{\text{cosec }40^\circ}{\sec50^\circ}-4 \cos50^\circ\text{cosec }40^\circ$
$ =\frac{\sin50^\circ}{\sin50^\circ}+\frac{\text{cosec }40^\circ}{\text{cosec }40^\circ}-4\frac{\cos50^\circ}{\cos50^\circ}$
$=1+1-4$
$=-2$

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