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Question
Without using trigonometric tables evaluate:
`(sin 65^@)/(cos 25^@) + (cos 32^@)/(sin 58^@) - sin 28^2. sec 62^@ + cosec^2 30^@`
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Solution
`(sin 65^@)/(cos 25^@) + (cos 32^@)/(sin 58^@) - sin 28^2. sec 62^@ + cosec^2 30^@`
`= (sin(90^@ - 25^@))/cos 25^@ + (cos (90^@ - 58^@))/sin 58^@ - sin 28^@ xx 1/(cos(90^@ - 28^@) ) + 1/sin^2 30`
`= cos 25^@/cos 25^@ + (sin 58^@)/(sin 58^@) - sin 28^@ xx 1/sin 28^@ + (1/(1/2)^2)`
= 1 + 1 - 1 + 4
= 5
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