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Question
Without using trigonometric tables evaluate
`(sin 35^@ cos 55^@ + cos 35^@ sin 55^@)/(cosec^2 10^@ - tan^2 80^@)`
Solution
`(sin 35^@ cos 55^@ + cos 35^@ sin 55^@)/(cosec^2 10^@ - tan^2 80)`
`= (sin 35^@ . cos (90^@ - 35^@) + cos 35^@. sin (90^@ - 35^@))/(cosec^2(90^@ - 80^@) - tan^2 80^@`)
`= (sin 35^@ . sin 35^@ + cos 35^@ . cos 35^@) /(sec^2 80^@ - tan^2 80^@)`
`= (sin^2 35^@ + cos^2 35^@)/(sec^2 80^@ - tan^2 80^@) = 1/1 = 1`
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