Find the exact value of the expression $\mathrm{tan}\left[{\mathrm{cos}}^{-1}(-\frac{\sqrt{3}}{2})\right]$ Do not use a calculator.

Tazmin Horton
2021-08-13
Answered

Find the exact value of the expression $\mathrm{tan}\left[{\mathrm{cos}}^{-1}(-\frac{\sqrt{3}}{2})\right]$ Do not use a calculator.

You can still ask an expert for help

coffentw

Answered 2021-08-14
Author has **103** answers

Consider the given inverse trigonometry $\mathrm{tan}\left[{\mathrm{cos}}^{-1}(-\frac{\sqrt{3}}{2})\right]$

As we know that

$\mathrm{cos}}^{-1}\frac{\sqrt{3}}{2}=\frac{5\pi}{6$

Then

$\mathrm{tan}\left[{\mathrm{cos}}^{-1}(-\frac{\sqrt{3}}{2})\right]=\mathrm{tan}\left[{\mathrm{cos}}^{-1}\mathrm{cos}\frac{5x}{6}\right]$

Use the formula${\mathrm{cos}}^{-1}\mathrm{cos}\theta =\theta$

$\mathrm{tan}\left[{\mathrm{cos}}^{-1}(-\frac{\sqrt{3}}{2})\right]=\mathrm{tan}\left[\frac{5\pi}{6}\right]$

$=-\frac{1}{\sqrt{3}}$

As we know that

Then

Use the formula

Jeffrey Jordon

Answered 2021-12-10
Author has **2027** answers

Answer is given below (on video)

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