Question

cos^2A+cos^2(A+60)+cos^2(A-60)=3/2

Answer 1

Hello user☺☺

It will be..

cos^2A + cos^2(A+60) + cos^2(A-60) = 3/2

cos^2A + cos^2Acos^2 60° - sin^2Asin^2 60° + cos^2Acos^2 60° + sin^2Asin^2 60° =3/2

cos^2A +2 × cos^2A × 1/4 = 3/2


3/2 cos^2A = 3/2

Cos^2A = 1

Cos A = 1 and -1

So, A = 90° or 270°


Hope it works☺☺

Answer 2

$\huge \color{pink}\underline \bold { \underline \color{plum} \mathcal{HEYA }}$

${cos}^{2} A + { \cos}^{2} (A + 60) + {cos}^{2} ( A - 60) = \frac{3}{2}$

Using the formula

$\small{\cos( \alpha + \beta ) = \cos( \alpha ) \cos( \beta ) - \sin( \alpha ) \sin( \beta )}$

and

$\small{\cos( \alpha - \beta ) = \cos( \alpha ) \cos( \beta ) + \sin( \alpha ) \sin( \beta ) }$

$\small{cos}^{2} A + {cos}^{2} A \: {cos}^{2} 60 \degree - {sin}^{2} A \: {sin}^{2} 60 \degree + {cos}^{2}A \: {cos}^{2} 60 \degree + {sin}^{2} A \: {sin}^{2} 60 \degree \: = \frac{3}{2}$

$\small {cos}^{2} A + \frac{1}{4} {cos}^{2} A + \frac{1}{4} {cos}^{2} A = \frac{3}{2}$

${cos}^{2} A(1 + \frac{1}{4} + \frac{1}{4} ) = \frac{3}{2}$

$\frac{3}{2} {cos}^{2} A = \frac{3}{2}$

${cos}^{2} A = 1 \implies \: cos \: A = + - 1$

$A = \color{green}90 \degree \: or \: 270 \degree$

Hope it helps ✌️ ✌️