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Question
Evaluate the Following
`sin 30^2/sin 45^@ + tan 45^@/sec 60^@ - sin 60^@/cot 45^@ - cos 30^@/sin 90^@`
Solution
`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`
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