The value of ²2π/15 - ²π/30 is:

Correct Answer is : 5−18{{5}-1}{8}85−1

Correct Answer is : 5−18{{5}-1}{8}85−1

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Trigonometry Practice Test 2

Question : 11 of 22

Marks: +1, -0

The value of

\sin^2\frac{2\pi}{15} - \sin^2\frac{\pi}{30}

is:

Solution:

Concept:

Use the identity

\sin^2 A - \sin^2 B = \sin(A+B)\sin(A-B)

Explanation:

Let

A=\frac{2\pi}{15}

and

B=\frac{\pi}{30}

Then

A+B=\frac{2\pi}{15}+\frac{\pi}{30}=\frac{\pi}{6}

Also

A-B=\frac{2\pi}{15}-\frac{\pi}{30}=\frac{\pi}{10}

So,

\sin^2\frac{2\pi}{15}-\sin^2\frac{\pi}{30}=\sin\frac{\pi}{6}\sin\frac{\pi}{10}

Now,

\sin\frac{\pi}{6}=\frac{1}{2}

and

\sin\frac{\pi}{10}=\frac{\sqrt{5}-1}{4}

Thus, the value is

\frac{1}{2}\times\frac{\sqrt{5}-1}{4}=\frac{\sqrt{5}-1}{8}

Answer:

\frac{\sqrt{5}-1}{8}

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