Question

Evaluate the Following

`sin 30^2/sin 45^@ + tan 45^@/sec 60^@ - sin 60^@/cot 45^@ - cos 30^@/sin 90^@`

Answer 1

`sin 30^2/sin 45^@ + tan 45^@/sec 60^@ - sin 60^@/cot 45^@ - cos 30^@/sin 90^@`    .....(1)

By trigonometric ratios we have

`sin 30^@  = 1/2      sin 45^@ = 1/sqrt2   tan 45^@ = 1    sec 60^@ = 2    sin 60^@ = sqrt3/2`

`cot 45^@ = 1        cos 30^@ = sqrt3/2     sin 90^@ = 1`

By substituting above values in (i), we get

`1/2 . sqrt2 + 1/2 - sqrt3/2 . 1 - sqrt3/2 . 1`

`= (2 + 1  (2/3))/2`