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Question
Find the value of x in the following :
cos 2x = cos 60° cos 30° + sin 60° sin 30°
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Solution
We have
cos 2x = cos 60° cos 30° + sin 60° sin 30°
Now we know that
`sin 60^2 = cos 30^@ = sqrt3/2 and sin 30^@ = cos 60^@ = 1/2`
Now by substituting above values in equation (1), we get,
`cos 2x = cos 60^@ cos 30^@ + sin 60^@ sin 30^@`
`cos 2x = 1/2 xx sqrt3/2 + sqrt3/2 xx 1/2`
`= sqrt3/4 + sqrt3/4`
`= (2sqrt3)/4`
Therefore
`cos 2x = (2sqrt3)/4`
Now `(2 sqrt3)/2` get reduced to `sqrt3/2`
Therefore
`cos 2x = sqrt3/2` ....(2)
Since
`cos 30^@ = sqrt3/2` .....(3)
Therefore by comparing equation (2) and (3)
We get
`2x = 30^@`
`=> x = 30^@/2`
Therefore
`x= 15^@`
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