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Trigonometric Identities

Solve: sin4...

Question

Solve: $s i n^{4} θ + 2 s i n^{2} θ c o s^{2} θ + c o s^{4} θ = 1$

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Solution

As $(a + b)^{2} = a^{2} + 2 a b + b^{2}$

We can write,
${sin}^{4} θ + 2 {sin}^{2} θ {cos}^{2} θ + {cos}^{4} θ = ({sin}^{2} θ + {cos}^{2} θ)^{2} = 1^{2} = 1$

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