Question

Prove that sin 18degree= root 5-1/4​

Answer 1

Answer:

Let θ=18. Then

5θ=90

∴2θ+3θ=90

⇒2θ=90−3θ

⇒sin2θ=sin(90−3θ)=cos3θ

⇒2sinθcosθ=4cos

3

θ−3cosθ

⇒2sinθcosθ−4cos

3

θ+3cosθ=0

⇒cosθ(2sinθ−4cos

2

θ+3)=0

⇒2sinθ−4(1−sin

2

θ)+3=0

⇒sinθ=

2×4

−2±

2

2

−4×4×(−1)

⇒sinθ=

8

−2±

20

⇒sinθ=

4

5

−1

∴sin18=

4

5

−1