How to solve

Question

sinΘ+sin²Θ=1   then cos²Θ+ cos⁴Θ=?

Answer 1

sin(x)+sin²(x)=1

sin²(x)+cos²(x)=1 is a trig identity

sin(x)+sin²(x)=sin²(x)+cos²(x)

sin(x)=cos²(x)

Looking at cos²(x)+cos⁴(x) we have:

sin(x)+[cos²(x)]²

sin(x)+[sin(x)]²

sin(x)+sin²(x) which equals 1 from your hypothesis above

Therefore cos²(x)+cos⁴(x)=1 also