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Find the value of cos15^(@) with the hel...

Find the value of `cos15^(@)` with the help of `cos 2A=2cos^(2)A-1`

Text Solution

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Let `A=15^(@)`
From the result `cos2A=2cos^(2)A-1`
`cos30^(@)=2cos^(2)15^(@)-1`
`=1+sqrt(3)/2=(2+sqrt(3))/2`
`rArr cos^(2)15^(@)=(2+sqrt(3))/(4)`
`rArr cos15^(@)=sqrt(2+sqrt(3))/(2)`
`therefore` cos is positive in 1st quadrant Ans.
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