Prove the following trigonometric identities-If a cos 3-3 a cos-sin 2-m- a sin 3-3 a cos 2-sin-n- prove that m-n2 - 3-m-n2 - 3-2 a2 - 3

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Implicit Differentiation

Prove the fol...

Question

Prove the following trigonometric identities.

If a cos³ θ + 3 a cos θ sin² θ = m, a sin³ θ + 3 a cos² θ sin θ = n, prove that (m + n)^2/3 + (m − n)^2/3 = 2a²^/3

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a {cos}^{3} θ + 3 a cos θ {sin}^{2} θ = m

a {sin}^{3} θ + 3 a sin θ {cos}^{2} θ = n

(m + n)^{\frac{2}{3}} + (m - n)^{\frac{2}{3}} = 2 a^{\frac{2}{3}}

a {cos}^{3} θ + 3 a cos θ {sin}^{2} θ = m

a {sin}^{3} θ + 3 a {cos}^{2} θ sin θ = n

{(m + n)}^{\frac{2}{3}} + {(m - n)}^{\frac{2}{3}}

{(\frac{x}{a})}^{2 / 3} + {(\frac{y}{b})}^{2 / 3} = 1

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