Question

find the value of √sin^4 22.5 + √4 cos^2 22.5 + √ cos^4 22.5 + √4 sin^2 22.5​

Answer 1

sin2(θ2)=1−cosθ2

substitutingθ=45∘

sin2(45∘2)=1−cos45∘2

⟹sin2(22.5∘)=1−12–√2

⟹sin2(22.5∘)=2–√−122–√

⟹sin2(22.5∘)=2−2–√4

⟹sin(22.5∘)=2−2–√−−−−−−√2