Question

Without using trigonometric tables, evaluate the following:

$\frac{\sec 37°}{\mathrm{cosec}53°}+2\cot 15°\cot 25°\cot 45°\cot 75°\cot 65°-3\left({\sin }^{2}18°+{\sin }^{2}72°\right)$

Answer 1

We have to evaluate the following expression

Here we are going to use following identities.

The given expression can be written as

Hence the value of the given expression is zero.