Prove that $(\mathrm{cos}A+\mathrm{sin}A)(\mathrm{cos}2A+\mathrm{sin}2A)=\mathrm{cos}A+\mathrm{sin}3A$

Gregory Emery
2022-01-17
Answered

Prove that $(\mathrm{cos}A+\mathrm{sin}A)(\mathrm{cos}2A+\mathrm{sin}2A)=\mathrm{cos}A+\mathrm{sin}3A$

You can still ask an expert for help

soanooooo40

Answered 2022-01-18
Author has **35** answers

Use following facts:

$\mathrm{cos}A\mathrm{sin}2A+\mathrm{sin}A\mathrm{cos}2A=\mathrm{sin}(A+2A)=\mathrm{sin}3A$

$\mathrm{cos}A\mathrm{cos}2A+\mathrm{sin}A\mathrm{sin}2A=\mathrm{cos}(2A-A)=\mathrm{cos}A$

asked 2021-08-20

Let P(x, y) be the terminal point on the unit circle determined by t. Then

asked 2022-03-01

So far I got

$r=\frac{7}{4-2\mathrm{cos}\theta}$

$(r(4-2\mathrm{cos}\theta )=7$

$r(4-2\left(\frac{x}{r}\right))=7$

asked 2022-04-28

Prove $\mathrm{sin}(\alpha -\beta )+\mathrm{sin}(\alpha -\gamma )+\mathrm{sin}(\beta -\gamma )=4\mathrm{cos}\frac{\alpha -\beta}{2}\mathrm{sin}\frac{\alpha -\gamma}{2}\mathrm{cos}\frac{\beta -\gamma}{2}$

asked 2022-03-27

How can I simplify $\mathrm{cos}\left(2x\right)+\frac{1}{2}\mathrm{sin}\left(4x\right)-\frac{1}{2}\mathrm{cos}\left(4x\right)$ into a single expression?

asked 2022-01-17

Finding n if $\left|\sum _{r=0}^{3n-1}{\beta}^{{2}^{r}}\right|=4\sqrt{2}$ where $\beta =\mathrm{exp}\left(\frac{i2\pi}{7}\right)$

asked 2022-03-15

What is the value of this trigonometric sum ratio:

$\frac{\sum _{n=1}^{44}{\mathrm{cos}n}^{\circ}}{\sum _{n=1}^{44}{\mathrm{sin}n}^{\circ}}=?$

asked 2022-01-25

Find $\mathrm{cot}\left(\sum _{n=1}^{23}{\mathrm{cot}}^{-1}(1+\sum _{k=1}^{n}2k)\right)$

I tried to simplify it but it became messy. How can I find$\sum _{n=1}^{23}{\mathrm{cot}}^{-1}(1+n+{n}^{2})?$

I tried to simplify it but it became messy. How can I find