Question

If 3sin^(2)x-7sin x +2=0, x in [0,(pi)/(2)] and
f(n)(theta)=sin^(n) theta + cos^(n) theta. On the basis of above information, the value of
( sin 5 x + sin 4 x)/( 1+ 2 cos 3 x) is:

Here I am not able to find the value of x
i got x = sin^-1(1/3)
What after that????
Please help

Answer 1

not sure what the f_{_k}(θ) has to do with anything here, but if sinx = 1/3 then cosx = √8/3
then you can use various multiple-angle formulas to find
sin5x and cos3x

and are those powers in parens exponents, or derivatives?
Usually f^⁽ⁿ⁾(x) is the nth derivative