Question

what is the value of sin(15/2)​

Answer 1

Answer:

Step-by-step explanation:

I am assuming that you know the value of sin30°.

Remember the identity,

Sin(2A)=2sinAcosA

Putting A=15° we get

Sin30°=2sin15°cos15° ==>(1)

One more identity,

Cos2A=1–2(sinA)² ==>(2)

Putting A=15° we get,

Cos30°=1–2sin²15°

Sin15°=[√(2-√3)]/2

Putting value of sin15° in (1) we get,

Cos15°=[ √(2+√3)]/2

Again using identity 2 and putting A=7.5°

Cos15°=1–2sin²7.5°

Sin7.5°=[√2-{√(2+√3)}]/2