Question

$\sf\:Cos^2 \theta + Cos^2 (60° + \theta) + Cos^2 (60° - \theta)$​

Answer 1

$\bf\large\textbf {\underline {\underline {Solution :-}}}\\ \\ \bf\large { = Cos^2 \theta + Cos^2 (60\degree + \theta) + Cos^2 (60\degree - \theta)} \\ \\ \bf\large { = Cos^2 \theta + [Cos (60\degree + \theta)]^2 + [Cos (60\degree - \theta)]^2} \\ \\ \bf\large { = Cos^2 \theta + [ Cos60\degree Cos\theta - Sin60\degree Sin\theta]^2 + [ Cos60\degree Cos\theta + Sin60\degree Sin\theta]^2} \\ \\ \bf\large { = Cos^2 \theta + 2 (\dfrac {1}{4} × Cos^2 \theta + \dfrac {3}{4} × Sin^2 \theta )} \\ \\ \bf\large { = Cos^2 \theta + \dfrac {Cos^2 \theta}{2} + \dfrac {3}{2} × Sin^2 \theta } \\ \\ \bf\large {= \dfrac {3Cos^2 \theta}{2} + \dfrac {3 Sin^2 \theta}{2}}\\ \\ \bf\large {= \dfrac {3}{2} ( Cos^2 \theta + Sin^2 \theta)} \\ \\ \qquad\large {\boxed {\bf {= \dfrac{3}{2}}}}$

Answer 2

Hey!

Refer attachment!