Evaluate each of the following: (cosec62 45° sec^2 30°) (sin^2 30° + 4 cot^2 45°- sec62 60°)

Question

Evaluate each of the following:

(cosec² 45° sec² 30°) (sin² 30° + 4 cot² 45°- sec² 60°)

Answer 1

(cosec² 45° sec² 30°) (sin² 30° + 4 cot² 45°- sec² 60°)

= \((2\times\frac{2}3)\)\((\frac{1}4+4\times1-4)\)

= \(\frac{4}3\)\((\frac{1}4+4\times1-4)\) = \(\frac{1}3\)