(i)
Since x lies in the 2nd quadrant, cos x is negative.
Thus,
Now, using the identity , we get
Since x lies in the 2nd quadrant and lies in the 1st quadrant, is positive.
Again,
Now,
(ii)
Now,
Hence, the value of tan 2x is .
(iii) and .
Since x lies in the 1st quadrant, cos x is positive.
Thus,
Now,
Hence, the value of sin 4x is .