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Question
Evaluate:
`(sin35^circ cos55^circ + cos35^circ sin55^circ)/(cosec^2 10^circ - tan^2 80^circ)`
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Solution
`(sin35^circ cos55^circ + cos35^circ sin55^circ)/(cosec^2 10^circ - tan^2 80^circ)`
= `(sin35^circ.cos(90^circ - 35^@) + cos35^circ.sin(90^circ - 35^circ))/(cosec^2(90^circ - 80^circ) - tan^2 80^circ)`
= `(sin35^circ.sin35^circ + cos35^circ.cos35^circ)/(sec^2 80^circ - tan^2 80^circ)`
= `(sin^2 35^circ + cos^2 35^circ)/(sec^2 80^circ - tan^2 80^circ)`
= `1/1`
= 1
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