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Question
Evaluate the Following:
`(tan^2 60^@ + 4 cos^2 45^@ + 3 sec^2 30^@ + 5 cos^2 90)/(cosec 30^@ + sec 60^@ - cot^2 30^@)`
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Solution
`(tan^2 60^@ + 4 cos^2 45^@ + 3 sec^2 30^@ + 5 cos^2 90)/(cosec 30^@ + sec 60^@ - cot^2 30^@)` ...(i)
By trigonometric ratios we have
`tan 60^@ = sqrt3 cos 45^@ = 1/sqrt2 sec 30^@ = 2/sqrt3`
`cos 90^@ = 0 cosec 30^@ = 2 sec 60^@ = 2 cot 30^@ = sqrt3`
By substituting above values in (i), we get
`((sqrt3)^2 + 4.(1/sqrt2)^2 + 2 + [2/sqrt3]^2 + 5(0)^2)/(2 + 2sqrt2 (+ sqrt3)^2)`
= `(3 + 4. 1/2 + 3 4/3)/(4 - 3)`
= `(3 + 2 + 4)/1`
= 9
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