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Question
Without using trigonometric tables, evaluate
`sin^2 34^@ + sin^2 56^@ + 2tan 18^@ tan 72^@ - cot^2 30^@`
Solution
`sin^2 34^@ + sin^2 56^@ + 2 tan 18^@ tan 72^@ - cot^2 30^@`:
`= sin^2 34^2 + sin^2 (90^@ - 34^@) + 2 tan 18^@ tan (90^@ - 18^@) - cot^2 30^@`
`= sin^2 34^@ + cos^2 34^@ + 2tan 18^@ cot 18^@ - cot^2 30^@`
`= (sin^2 34^@ + cos^2 34^@) + 2 tan 18^@ xx 1/(tan 18^@) - cot^2 30^@`
`= 1 + 2 xx 1 - (sqrt3)^2`
= 1 + 2 - 3
= 3 - 3
= 0
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