prove- cos2(pi /8) + cos2 (3pi / 8) +cos2(5pi / 8) +cos2 (7pi / 8) = 2 - Maths - Trigonometric Functions

Question

prove-
cos2(pi /8) + cos2 (3pi / 8)
+cos2(5pi / 8) +cos2 (7pi / 8) = 2

Ankush Jain · Accepted Answer

To prove: $\cos^{2} \frac{π}{8} + \cos^{2} \frac{3 π}{8} + \cos^{2} \frac{5 π}{8} + \cos^{2} \frac{7 π}{8} = 2$ Proof: $L H S = \cos^{2} \frac{π}{8} + \cos^{2} \frac{3 π}{8} + \cos^{2} (π - \frac{3 π}{8}) + \cos^{2} (π - \frac{π}{8}) = \cos^{2} \frac{π}{8} + \cos^{2} \frac{3 π}{8} + \cos^{2} (\frac{3 π}{8}) + \cos^{2} (\frac{π}{8}) = 2 (\cos^{2} \frac{π}{8} + \cos^{2} \frac{3 π}{8}) = 2 (\cos^{2} \frac{π}{8} + \cos^{2} (\frac{π}{2} - \frac{π}{8})) = 2 (\cos^{2} \frac{π}{8} + \sin^{2} \frac{π}{8}) = 2 = R H S$ [Hence proved]