Solve Exponential Equation For x

2^(sin^2(x)) +2^(cos^2(x)) = 3...........2^x =3 for x = log(3)/log(2)=>2^( log(3)/log(2))=3

2^(sin^2(x)) +2^(cos^2(x)) = 2^( log(3)/log(2)).........bases are same, exponents must be same too
sin^2(x) +cos^2(x) = log(3)/log(2)
1 = 3.....................(no solutions exist)


but, if x=0 equation is true

2^(sin^2(0)) +2^(cos^2(0)) = 3..........true

or if you write it in this form
you also have x ≈ -37.6991118430775

.......true

 

Excellent.

Try this one:

Solve Trigonometric System