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Q. 3

Expert-verified
Found in: Page 500

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

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# find the exact value of the expression sin 285$°$sin 75$°$

$\mathrm{sin}285°\mathrm{sin}75°=-0.9330127019$

See the step by step solution

## Step 1. Rewriting the expression

sin(270$°$+x)=$-$cos(x )

sin285$°$=sin(270$°$+15$°$) =$-\mathrm{cos}\left(15°\right)$

Given expression becomes

sin 285$°$sin 75$°$= $-$cos15$°$sin75$°$

## Step 2. Calculations

cos(90$°$$-$x)=sin(x)

so, sin75$°$=cos(90$°-$75$°$)=cos15$°$

So now the expression becomes

$-$cos15 $°$cos15$°$=$-{\mathrm{cos}}^{2}\left(15°\right)$

We know that

cos(2x)= $2{\mathrm{cos}}^{2}x-1$

role="math" localid="1646416466227"

Therefore,role="math" localid="1646416523469" $\mathrm{sin}285°\mathrm{sin}75°=-0.9330127019$

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