Question

prove that cos2° 72° - sin 54 degrees = √5/4​

Answer 1

Answer:

Here, we will use, sin18∘=5–√−14

sin2(72∘)−sin2(60∘)

=sin2(90∘−18∘)−sin2(60∘)

=cos2(18∘)−sin2(60∘)

=1−sin2(18∘)−sin2(60∘)

Putting values of sin18∘andsin60∘

=1−(5–√−14)2−(3–√2)2

=1−(6−25–√16)−34

=16−6+25–√−1216

=25–√−216

∴sin2(72∘)−sin2(60∘)=5–√−18