Emanuel Keith
2022-06-24
Answered

Prove that ${\mathrm{sin}}^{6}\frac{\theta}{2}+{\mathrm{cos}}^{6}\frac{\theta}{2}=\frac{1}{4}(1+3{\mathrm{cos}}^{2}\theta )$

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asked 2021-08-20

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

asked 2022-04-27

Simplify $\mathrm{tan}\left(2\mathrm{arcsin}\left(\frac{1}{3}\right)\right)$

$\mathrm{tan}\left(2\mathrm{arcsin}\left(\frac{1}{3}\right)\right)$

$=\mathrm{tan}\left(2{\mathrm{sin}}^{-1}\left(\frac{1}{3}\right)\right)$

$={\mathrm{tan}}^{-1}\left(2\mathrm{sin}\left(\frac{1}{3}\right)\right)$

asked 2022-04-25

Solve this equation.

${\left(\sqrt{\sqrt{2}+1}\right)}^{\mathrm{sin}\left(x\right)}+{\left(\sqrt{\sqrt{2}-1}\right)}^{\mathrm{sin}\left(x\right)}=2$

asked 2022-01-28

I need to find real, imaginary parts of $\mathrm{tan}(x+yi)$ and the modulus of it. I have:

$Re\left(\mathrm{tan}(x+yi)\right)=\frac{\mathrm{sin}2x}{\mathrm{cos}2x+\text{cosh}2x}$

and

$Im\left(\mathrm{tan}(x+yi)\right)=\frac{\text{sinh}2y}{\mathrm{cos}2x+\text{cosh}2x}$

I know that$\left|Z\right|=\sqrt{R{e}^{2}+I{m}^{2}}$ But when I calculate with the results Ive

and

I know that

asked 2022-06-11

Prove that: $\frac{4({\mathrm{cos}}^{4}\frac{\pi}{8}+{\mathrm{cos}}^{4}\frac{3\pi}{8})}{{\mathrm{cos}}^{4}\frac{7\pi}{8}-{\mathrm{cos}}^{4}\frac{11\pi}{8}}=\dots $

asked 2021-08-22

Prove that:

$(1+\frac{1}{{\mathrm{tan}}^{2}A})(1+\frac{1}{{\mathrm{cot}}^{2}A})=\frac{1}{{\mathrm{sin}}^{2}A-{\mathrm{sin}}^{4}A}$

asked 2021-08-11

Use the sum and difference identites to find the exact values of sine, cosine, tangent of the angle $\frac{7\pi}{12}$