Question

if sin squared theta + 3 cos theta is equal to 2 then find the value of cos cube theta + sec cube theta

Answer 1

sin^2 X + 3 cos X = 2
sin^2 X + 3 cos X = (sin^2 X + cos^2 X) +1
cos^2 X - 3 cos X = -1
cosX (cosX - 3)= -1

cos X= -1 (Max value of cos is 1, therefore other value is neglected)
X= nπ ,n=1,2,3,---------

substitute the value of X based on the range