Question

Find the general solution of the equation `3^(sin2x+2cos^2x)+3^(1-sin2x+2sin^2x)=28`
A. 3
B. 4
C. 5
D. 6

Answer 1

Correct Answer - B
`3^(sin 2x + 2cos^(2)x)+3^(1+2(1-cos^(2)x)-sin 2x)=28`
`rArr 3^(sin 2 x + 2 cos^(2)x)+(27)/(3^(sin 2x + 2 cos^(2)x))=28`
`rArr (3^(t))^(2)-28(3^(t))+27=0 rArr 3^(t)=27` or 1 `rArr 2x + 2 cos^(2)x=0` or 3 (not possible)
`rArr sin 2x + 2 cos^(2) x =0`
`rArr sin 2x + cos 2x =-1`
`rarr 4x = n pi, n in Z`
`rArr x = (3pi)/(4),(7pi)/(4),(pi)/(2),(3pi)/(2)`