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Trigonometric Ratios of Allied Angles

Solve sin2π...

Question

Solve ${sin}^{2} \frac{π}{4} + {sin}^{2} \frac{3 π}{4} + {sin}^{2} \frac{5 π}{4} + {sin}^{2} \frac{7 π}{4}$

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Solution

We know, that $sin \frac{3 π}{4} = sin (\frac{π}{2} + \frac{π}{4}) = cos \frac{π}{4} sin \frac{5 π}{4} = sin (\frac{3 π}{2} - \frac{π}{4}) = - cos \frac{π}{4} sin \frac{7 π}{4} = sin (2 π - \frac{π}{4}) = - sin \frac{π}{4}$

Now, ${sin}^{2} \frac{π}{4} + {sin}^{2} \frac{3 π}{4} + {sin}^{2} \frac{5 π}{4} + {sin}^{2} \frac{7 π}{4} = {sin}^{2} \frac{π}{4} + {cos}^{2} \frac{π}{4} + {cos}^{2} \frac{π}{4} + {sin}^{2} \frac{π}{4} = 1 + 1 = 2$

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Similar questions

s i n^{2} (\frac{π}{4}) + s i n^{2} (\frac{3 π}{4}) + s i n^{2} (\frac{5 π}{4}) + s i n^{2} (\frac{7 π}{4})

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Q. The value of

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

{sin}^{2} \frac{π}{8} + {sin}^{2} \frac{3 π}{8} + {sin}^{2} \frac{5 π}{8} + s i n^{2} \frac{7 π}{8} = 2

Q. The value of

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

Q. Prove sin2 π/8 + sin2 3π/8 + sin2 5π/8 + sin2 7π/8 = 2

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