Prove- sin2-cos4-cos2-sin4-

LHS=sin ^ 2 θ #160; +cos ^ 4 θ #160; =1 cos ^ 2 θ #160; + (cos ^ 2 θ #160; ) ^ 2 =1 cos ^ 2 θ #160; + (1 sin ^ 2 θ #160; ) ^ 2 ...

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Proof by mathematical induction

Prove: sin2θ...

Question

Prove:
${sin}^{2} θ + {cos}^{4} θ = {cos}^{2} θ + {sin}^{4} θ$

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Solution

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\frac{{cos}^{2} θ}{a} = \frac{{sin}^{2} θ}{b}

\frac{{cos}^{4} θ}{a} + \frac{{sin}^{4} θ}{b} =

\frac{c o s θ + c o s 2 θ + c o s 3 θ + c o s 4 θ}{s i n θ + s i n 2 θ + s i n 3 θ + s i n 4 θ} = c o t \frac{5 θ}{2}

{tan}^{2} 2^{\circ} + {tan}^{2} 4^{\circ} + \dots + {tan}^{2} 88^{\circ} = a,

89^{\circ} \sum θ = 1^{\circ} \frac{{sin}^{4} θ + {cos}^{4} θ}{{sin}^{2} θ {cos}^{2} θ}

sin θ + {sin}^{2} θ = 1

{cos}^{2} θ + {cos}^{4} θ = 1

(sin θ + csc θ)^{2} = {sin}^{2} θ + {csc}^{2} θ + 2

{cos}^{4} θ - {sin}^{4} θ = 1 - 2 {sin}^{2} θ

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