Question

${ \sin}^{2} \alpha + { \sin}^{2}(120 - \alpha ) + { \sin}^{2}(120 + \alpha ) = \frac{3}{2 } \\ \\ prove \: it$
prove it
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Answer 1

Sine and cosine \sin(\theta) = \cos(90^\circ-\theta)sin(θ)=cos(90

∘

−θ)sine, left parenthesis, theta, right parenthesis, equals, cosine, left parenthesis, 90, degree, minus, theta, right parenthesis

\cos(\theta) = \sin(90^\circ-\theta)cos(θ)=sin(90

∘

−θ)cosine, left parenthesis, theta, right parenthesis, equals, sine, left parenthesis, 90, degree, minus, theta, right parenthesis

Tangent and cotangent \tan(\theta) = \cot(90^\circ-\theta)tan(θ)=cot(90

∘

−θ)tangent, left parenthesis, theta, right parenthesis, equals, cotangent, left parenthesis, 90, degree, minus, theta, right parenthesis

\cot(\theta) = \tan(90^\circ-\theta)cot(θ)=tan(90

∘

−θ)cotangent, left parenthesis, theta, right parenthesis, equals, tangent, left parenthesis, 90, degree, minus, theta, right parenthesis

Secant and cosecant \sec(\theta) = \csc(90^\circ-\theta)sec(θ)=csc(90

∘

−θ)