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Find the value of 2cos((5pi)/12) cos(pi/...

Find the value of `2cos((5pi)/12) cos(pi/12)` and `2sin((5pi)/12)cos(pi/12)`

Text Solution

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(i) On using the formula,

`=2 cos A cos B=cos (A+B)+cos (A-B)`

`=(2 cos (5 pi)) / (12) cos pi / 12=cos ((5 pi) / 12+pi / 12)+cos ((5 pi) / 12-pi / 12)`

`=cos ((6 pi) / (12))+cos ((4 pi) / (12))`

`=cos (pi / 2)+cos (pi / 3)`

`=cos (180^{circ} / 2)+cos (180^{circ} / 3) `

`=cos 90^{circ}+cos 60^{circ}`

`=0+1 / 2`

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