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Prove that: sin(8pi)/3cos(23pi)/6+cos(13...

Prove that: `sin(8pi)/3cos(23pi)/6+cos(13pi)/3sin(35pi)/6=1/2`

Text Solution

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Consider LHS
`sin(8pi)/3cos(23pi)/6+cos(13pi)/3sin(35pi)/6`
`=sin 480° * cos 690° + cos 780° * sin 1050°`
`=sin (90° × 5 + 30°) * cos (90° × 7 + 60°) + cos (90° × 8 + 60°) * sin (90° × 11 + 60°)`
As we know that when n is odd, sin → cos and cos → sin
Therefore LHS
`= cos 30° sin 60° + cos 60° [-cos 60°]`
`=sqrt 3/2 xx sqrt 3/2 - 1/2 xx 1/2`
`=3/4 - 1/4` ...
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