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If cosϕ = p/q and sinθ = r/s , then, find the value of sin(θ – ϕ)?

If cosϕ = p/q and sinθ = r/s , then, find the value of sin(θ – ϕ)? Correct Answer [rp - √{(s<span style="position: relative; line-height: 0; vertical-align: baseline; top: -0.5em;font-size:10.5px;">2</span> – r<span style="position: relative; line-height: 0; vertical-align: baseline; top: -0.5em;font-size:10.5px;">2</span>)(q<span style="position: relative; line-height: 0; vertical-align: baseline; top: -0.5em;font-size:10.5px;">2</span> – p<span style="position: relative; line-height: 0; vertical-align: baseline; top: -0.5em;font-size:10.5px;">2</span>)}]/qs

Given:

cosϕ = p/q and sinθ = r/s

Formula Used:

sin(x – y)  = sinxcosy - sinycosx

Calculation:

/qs

⇒ /qs

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