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How would you solve: sin^2(pi/5)-cos^2(pi/5)? (show steps) Thanks

1 Answer

Shwetank Mauria

Aug 10, 2018

${sin}^{2} (\frac{π}{5}) - {cos}^{2} (\frac{π}{5}) = \frac{1 - \sqrt{5}}{4}$ $sin^2(pi/5)-cos^2(pi/5)=(1-sqrt5)/4$

Explanation:

As ${cos}^{2} A - {sin}^{2} A = cos 2 A$ $cos^2A-sin^2A=cos2A$ ,

${sin}^{2} (\frac{π}{5}) - {cos}^{2} (\frac{π}{5})$ $sin^2(pi/5)-cos^2(pi/5)$

= $- cos (\frac{2 π}{5})$ $-cos((2pi)/5)$

= $- {cos 72}^{\circ}$ $-cos72^@$

= $- \frac{\sqrt{5} - 1}{4}$ $-(sqrt5-1)/4$ (see here )

= $\frac{1 - \sqrt{5}}{4}$ $(1-sqrt5)/4$

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