Could you solve it from opposite?

agreseza
2021-12-27
Answered

Prove that $\mathrm{sin}x+\mathrm{cos}x=\sqrt{2}\mathrm{sin}(x+\frac{\pi}{4})$

$\sqrt{2}(x+\frac{\pi}{4})=\sqrt{2}(\mathrm{sin}x\mathrm{cos}\frac{\pi}{4}+\mathrm{cos}x\mathrm{sin}\frac{\pi}{4})=\mathrm{sin}x+\mathrm{cos}x$

Could you solve it from opposite?

$\mathrm{sin}x+\mathrm{cos}x=\sqrt{2}\mathrm{sin}(x+\frac{\pi}{4})$

Could you solve it from opposite?

You can still ask an expert for help

Paul Mitchell

Answered 2021-12-28
Author has **40** answers

Hint:

yotaniwc

Answered 2021-12-29
Author has **34** answers

From

and

(both of which identities I assume as known and will not prove here), we obtain

and by adding (1)+(3),

Substitue

nick1337

Answered 2022-01-08
Author has **510** answers

Using the formula

See for first line we know

So the expression reduces to

Now I hope you can reduce it to second line.

For the second line use the formula I gave in starting of answer.

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