Question

Evaluate the following

`sin^2 30° cos^2 45 ° + 4 tan^2 30° + 1/2 sin^2 90° − 2 cos^2 90° + 1/24 cos^2 0°`

Answer 1

`sin^2 30° cos^2 45 ° + 4 tan^2 30° + 1/2 sin^2 90° − 2 cos^2 90° + 1/24 cos^2 0°`  ....(i)

By trigonometric ratios we have

`sin 30^@ = 1/2`   `cos 45^@ = 1/sqrt2`  `tan 30^2 = 1/sqrt3`  `sin 90^@ = 1    cos 90^@ = 0        cos 0^@ = 1`

By substituting above values in (i), we get

`[1/2]^2 . [1/sqrt2]^2 + 4[1/sqrt3]^2 + 1/2[1]^2 - 2[0]^2 + 1/24 [1]^2`

`1/4.1/2 + 4/ 1/3 + 1/2 - 0 + 1/24`

`1/8 + 4/3 + 1/2 + 1/24 = 48/24 = 2`