The number of values of `theta` in the range `[0, 2pi]` satisfying the equation `cos^4 2theta + 2 sin^2 2theta = 17(sintheta + costheta)^8` is

Answer

4

Explanation

Put `sin2theta=x` given equation becomes `x^(4)+117(1+2x+x^(2))^(2)`
Divide by `x^(2)`, we have `x^(2)+1/(x^(2))=17(x+1/x+2)`
Now put `y=x+1/ximpliesy=-7/4` or `-5/2`
Now `u=-7/4` have no soluton and `y=-5/2`, we have `x=-1/2,-2`
So, there are (4) solution in`[0,2pi]`