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Question
Find the value of x in the following :
`sqrt3 tan 2x = cos 60^@ + sin45^@ cos 45^@`
Solution
We have
`sqrt3 tan 2x = cos 60^@ + sin45^@ cos 45^@` .......(1)
Now we know that
`sin 45^@ = cos 45^@ = 1/sqrt2 and cos 60^@ = 1/2`
Now by substituting above values in equation (1), we get,
`sqrt3 tan 2x = cos 60^@ + sin 45^@ cos 45^@`
`sqrt3 tan 2x = 1/2 + 1/sqrt2 xx 1/sqrt2`
`= 1/2 + 1/(sqrt2 xx sqrt2)`
`=1/2 + 1/2`
`= (1 + 1)/2`
`= 2/2`
= 1
Therefore,
`sqrt3 tan 2x = 1`
`=> tan 2x = 1/sqrt3` .....(2)
Since
`tan 30^@ = 1/sqrt3` .....(3)
Therefore by comparing equation (2) and (3)
We get
`2x = 30^@`
`x = 30^@/2`
`=> x = 15^@`
x = 15
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