Value of sin 4 - 8 -sin 4 3- 8 -sin 4 5- 8 -sin 4 7- 8 is equal to-

The correct option is D 3/2 sin^4π8+sin^43π4+sin^45π8+sin^47pi8 =(sin^2π8)^2+(sin^23π8)^2+(sin^25π8)^2+(sin^27π8)^2 =(1 cosπ42)^2+(1 cos3π42)^2+( ...

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Composition of Inverse Trigonometric Functions and Trigonometric Functions

Value of si...

Question

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:

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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} =

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)]

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

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

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)]

{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}

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