"Multiply and simplify: (sin⁡θ+cos⁡θ)(sin⁡θ+cos⁡θ)−1sin⁡θcos⁡θ" was answered by our community

Rui Baldwin

Answered question

2021-02-21

Multiply and simplify:

\frac{(\sin θ + \cos θ) (\sin θ + \cos θ) - 1}{\sin θ \cos θ}

Liyana Mansell

Skilled2021-02-22Added 97 answers

Use the square of a binomal:

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

= \frac{(\sin^{2} θ + 2 \sin \cos θ + \cos^{2} θ) - 1}{\sin θ \cos θ}

= \frac{(2 \sin θ \cos θ + \sin^{2} θ + \cos^{2} θ) - 1}{\sin θ \cos θ}

Use the Pythagorean identity:

\sin^{2} θ + \cos^{2} θ = 1

= \frac{(2 \sin θ \cos θ + 1) - 1}{\sin θ \cos θ}

Simplify:

\frac{2 \sin θ \cos θ}{\sin θ \cos θ} = 2

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