Monique Slaughter

2021-12-31

Find the value of the expression

when

I don't know if I am supposed to simplify the given expression, but I just put α=60∘ to get

What can I do next?

Mary Goodson

Beginner2022-01-01Added 37 answers

This seems to be a simpler question than what is thought to be.

Replace$\alpha$ with $60}^{\circ$ , just remember

${\mathrm{sin}30}^{\circ}=\frac{12}{,}\text{}\text{}{\mathrm{sin}}^{2}x+{\mathrm{cos}}^{2}x=1$

Then,

$\mathrm{sin}15}^{\circ}{\mathrm{sin}15}^{\circ}+{\mathrm{cos}}^{2}{15}^{\circ}-2{\mathrm{sin}30}^{\circ$

$=1-2\cdot \frac{12}{=}0$

Replace

Then,

Suhadolahbb

Beginner2022-01-02Added 32 answers

HINT

You could first use the following formula, known as one of the product to sum formulae among other names,

$\mathrm{sin}x\mathrm{sin}y\equiv \frac{12}{\mathrm{cos}(x-y)-\mathrm{cos}(x+y)}$

to evaluate$\mathrm{sin}15}^{\circ}{\mathrm{sin}105}^{\circ$ without having to explicitly evaluate $\mathrm{sin}15}^{\circ}\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}{\mathrm{sin}105}^{\circ$

You could then use the double angle formula for$\mathrm{cos}$ to write $\mathrm{cos}215}^{\circ$ in terms of $\mathrm{cos}30}^{\circ$

You could first use the following formula, known as one of the product to sum formulae among other names,

to evaluate

You could then use the double angle formula for

Vasquez

Expert2022-01-08Added 669 answers

Hint: Notice that

And,

If you do it this way, you won't have to calculate trigonometric ratios for

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