Find the exact value of the expression.

ringearV
2021-03-06
Answered

Find the exact value of the expression.

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Macsen Nixon

Answered 2021-03-07
Author has **117** answers

40

use the identity:

where:

Therefore,

Result:

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If $\mathrm{sin}x+\mathrm{sin}y=a{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\mathrm{cos}x+\mathrm{cos}y=b$ then find $\mathrm{tan}(x-\frac{y}{2})$

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Find the value of x from $\mathrm{sin}x+\mathrm{cos}x=\sqrt{2}\mathrm{sin}\left(5x\right)$

I used auxiliary argument method and converted into$\mathrm{cos}(\frac{\pi}{4}-x)=\mathrm{cos}(\frac{\pi}{2}-5x)$ (by introducing $\sqrt{2}$ as auxiliary argument and then using $\mathrm{cos}\left(\frac{\pi}{4}\right)\mathrm{cos}x+\mathrm{sin}\left(\frac{\pi}{4}\right)\mathrm{sin}x=\mathrm{cos}(\frac{\pi}{4}-x)$ and using $\mathrm{sin}5x=\mathrm{cos}(\frac{\pi}{2}-5x)$

But the answer isn't matching after using the formula for$\mathrm{cos}\theta =\mathrm{cos}\alpha$

I used auxiliary argument method and converted into

But the answer isn't matching after using the formula for

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