Sin4 -8-sin4 3-8-sin4 5-8-sin4 7-8-

Sin^4 π/4+sin^4 3π/8+sin^4 5π/8+sin^4 7π/8 =1/4[(2 sin^2 π/8)^2+(2 sin^2 3π/8)^2]+1/4[(2 sin^2 π/8)^2+(2 sin^2 3π/8)^2] =1/4[(1 cos π/4)^2+(1 cos 3π/4)^2]+1/4[( ...

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Byju's Answer

Standard XII

Mathematics

Trigonometric Ratios of Multiples of an Angle

sin4 π/8+sin4...

Question

$s i n^{4} \frac{π}{8} + s i n^{4} \frac{3 π}{8} + s i n^{4} \frac{5 π}{8} + s i n^{4} \frac{7 π}{8} =$

\frac{1}{2}

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\frac{1}{4}

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\frac{3}{2}

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\frac{3}{4}

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Solution

The correct option is C $\frac{3}{2}$
$s i n^{4} \frac{π}{4} + s i n^{4} \frac{3 π}{8} + s i n^{4} \frac{5 π}{8} + s i n^{4} \frac{7 π}{8}$
$= \frac{1}{4} [{(2 s i n^{2} \frac{π}{8})}^{2} + {(2 s i n^{2} \frac{3 π}{8})}^{2}] + \frac{1}{4} [{(2 s i n^{2} \frac{π}{8})}^{2} + {(2 s i n^{2} \frac{3 π}{8})}^{2}]$
$= \frac{1}{4} [{(1 - c o s \frac{π}{4})}^{2} + {(1 - c o s \frac{3 π}{4})}^{2}] + \frac{1}{4} [{(1 - c o s \frac{π}{4})}^{2} + {(1 - c o s \frac{3 π}{4})}^{2}]$
$= \frac{1}{4} [{(1 - \frac{1}{\sqrt{2}})}^{2} + {(1 + \frac{1}{\sqrt{2}})}^{2}] + \frac{1}{4} [{(1 - \frac{1}{\sqrt{2}})}^{2} + {(1 + \frac{1}{\sqrt{2}})}^{2}]$
$= \frac{1}{4} (3) + \frac{1}{4} (3) = \frac{3}{2} .$

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Similar questions

Q. Value of

{sin}^{4} \frac{π}{8} + {sin}^{4} \frac{3 π}{8} + {sin}^{4} \frac{5 π}{8} + {sin}^{4} \frac{7 π}{8}

is equal to:

Q. The expression

3 [{sin}^{4} {\frac{3}{2} π - α} + {sin}^{4} (3 π + α)] - 2 [{sin}^{6} {\frac{1}{2} π + α} + {sin}^{6} (5 π - α)]

is equal to

Q. Prove that

{sin}^{4} \frac{π}{8} + {sin}^{4} \frac{3 π}{8} + {sin}^{4} \frac{5 π}{8} + {sin}^{4} \frac{7 π}{8} = \frac{3}{2}

Q. Evaluate:

\int_{1}^{4} (c o s x - \frac{3}{x^{5}}) d x

2 ({sin}^{6} A + {cos}^{6} A) - 3 ({sin}^{4} A + {cos}^{4} A) + 1 = 0.

Another form :
The expression

3 [{sin}^{4} (\frac{3}{2} π - α) + {sin}^{4} (3 π + 4)] - 2 [{sin}^{6} (\frac{1}{2} π + α) + {sin}^{6} (5 π - α)]

is equal to

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sin4 π8+sin4 3π8+sin4 5π8+sin4 7π8=

The correct option is C 32sin4 π4+sin4 3π8+sin4 5π8+sin4 7π8 =14[(2 sin2 π8)2+(2 sin2 3π8)2]+14[(2 sin2 π8)2+(2 sin2 3π8)2] =14[(1−cos π4)2+(1−cos 3π4)2]+14[(1−cos π4)2+(1−cos 3π4)2] =14[(1−1√2)2+(1+1√2)2]+14[(1−1√2)2+(1+1√2)2] =14(3)+14(3)=32.

$s i n^{4} \frac{π}{8} + s i n^{4} \frac{3 π}{8} + s i n^{4} \frac{5 π}{8} + s i n^{4} \frac{7 π}{8} =$