Question

Class 11th
Prove that

cos²A + cos²(A+2π/3) + cos²(A - 2π/3) = 3/2

Answer 1

Recall the identity $x^2+y^2=(x+y)^2-2xy$

$\cos^2A+\cos^2(A+2\pi/3)+\cos^2(A-2\pi/3)$

$=\cos^2A+(\cos(A+2\pi/3)+\cos(A-2\pi/3))^2-2\cos(A+2\pi/3)\cos(A-2\pi/3)$

$=\cos^2A+(2\cos{A}*\cos(2\pi/3))^2-2(\cos^2A-\sin^2(2\pi/3))$

$=\cos^2A+(2\cos{A}*\frac{1}{2})^2-2(\cos^2A-\left(\frac{\sqrt{3}}{2}\right)^2)$

$=\cos^2A+\cos^2A-2(\cos^2A-\left(\frac{\sqrt{3}}{2}\right)^2)$

$=2\cos^2A-2\cos^2A+2*\frac{3}{4}$

$=\frac{3}{2}$

Answer 2

Answer:

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