Question

Find the value of x in the following :

cos 2x = cos 60° cos 30° + sin 60° sin 30°

Answer 1

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^@`