We have an answer to "If sinθ-cosθ=12then find the value of sinθ+cosθ."

Joyce Decker

Answered question

2023-03-13

\sin θ - \cos θ = \frac{1}{2}

then find the value of

\sin θ + \cos θ

helixl3u

Beginner2023-03-14Added 6 answers

Discover the value of the provided expression.
We have:

\sin θ - \cos θ = \frac{1}{2}

.
To find:

\sin θ + \cos θ

The result of squaring the two sides of the given equation is,

{(\sin θ - \cos θ)}^{2} = {(\frac{1}{2})}^{2} \Rightarrow \sin^{2} θ + \cos^{2} θ - 2 \sin θ \cos θ = \frac{1}{4} \Rightarrow 1 - 2 \sin θ \cos θ = \frac{1}{4} [∵ \sin^{2} θ + \cos^{2} θ = 1] \Rightarrow 2 \sin θ \cos θ = 1 - \frac{1}{4} \Rightarrow 2 \sin θ \cos θ = \frac{3}{4}

Now, on squaring the expression

\sin θ + \cos θ

.we get,

{(\sin θ + \cos θ)}^{2} = \sin^{2} θ + \cos^{2} θ + 2 \sin θ \cos θ \Rightarrow \sin θ + \cos θ = \sin^{2} θ + \cos^{2} θ + 2 \sin θ \cos θ \Rightarrow \sin θ + \cos θ = 1 + 2 \sin θ \cos θ [∵ \sin^{2} θ + \cos^{2} θ = 1] \Rightarrow \sin θ + \cos θ = 1 + \frac{3}{4} \Rightarrow \sin θ + \cos θ = \frac{7}{4} \Rightarrow \sin θ + \cos θ = \frac{7}{2}

Thus, the value of

\sin θ + \cos θ

\frac{7}{2}

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