I tried dividing both sides with

Dowqueuestbew1j
2021-12-27
Answered

Solve this trigonometric equation $\mathrm{sin}2x-\sqrt{3}\mathrm{cos}2x=2$

I tried dividing both sides with$\mathrm{cos}2x$ but then I win $\frac{2}{\mathrm{cos}2x}$

I tried dividing both sides with

You can still ask an expert for help

sukljama2

Answered 2021-12-28
Author has **33** answers

I hope you can solve further.

abonirali59

Answered 2021-12-29
Author has **35** answers

MySolution:: Given $\mathrm{sin}2x-\sqrt{3}\mathrm{cos}2x=2$

We can write it as

$\mathrm{sin}2x\cdot \frac{12}{-}\mathrm{cos}2x\cdot \frac{\sqrt{3}}{2}=1\Rightarrow \mathrm{sin}(2x-\frac{\pi}{3})=1=\mathrm{sin}\frac{\pi}{2}$

Above we have used the formula

$\mathrm{sin}\alpha \cdot \mathrm{cos}\beta -\mathrm{cos}\alpha \cdot \mathrm{sin}\beta =\mathrm{sin}(\alpha -\beta )$

So

$2x-\frac{\pi}{3}=n\pi +{(-1)}^{n}\cdot \frac{\pi}{2}\Rightarrow x=\frac{n\pi}{2}+{(-1)}^{n}\cdot \frac{\pi}{4}+\frac{\pi}{6}$

Where$n\in \mathbb{Z}$

We can write it as

Above we have used the formula

So

Where

nick1337

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

Divide by 2 to get

then find an angle y for which

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Double Angle Formulas: Finding $\mathrm{tan}2\theta$

I am trying to find$\mathrm{tan}2\theta$ where $\mathrm{sin}\theta =\frac{5}{13}$ and $\theta$ is in Quadrant One.

According to my textbook,$\mathrm{tan}2\theta =\frac{120}{119}$ , but I get $\frac{-10}{13}$ instead.

The Identity I am using:

$\mathrm{tan}2\theta =\frac{2\mathrm{tan}\theta}{1-{\mathrm{tan}}^{2}\theta}$

I am trying to find

According to my textbook,

The Identity I am using: