Question

Evaluate tan(cos^-1 8/17)

Answer 1

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Answer 2

The given inverse trigonometric function:

$\tan (\cos^{-1} \dfrac{8}{17})$

We have to find, the value of $\tan (\cos^{-1} \dfrac{8}{17})$ is:

Solution:

Let $\cos^{-1} \dfrac{8}{17}$ = θ

⇒ $\cos \theta=\dfrac{8}{17}$

We know that,

$\cos \theta=\dfrac{b}{h}=\dfrac{8}{17}$

Where, b = base and h = hypotaneous

∴ Perpendicular, p = $\sqrt{h^{2}-p^{2} }$

= $\sqrt{17^{2}-8^{2} }$

= $\sqrt{289-64}$

= $\sqrt{225}$

= 15

$\cos \theta=\dfrac{p}{b}=\dfrac{15}{8}$

⇒ θ = $\tan^{-1} \dfrac{15}{8}$

∴ $\tan (\tan^{-1} \dfrac{15}{8})$ [ ∵  $\tan (\tan^{-1} \theta)$ = θ]

= $\dfrac{15}{8}$

∴ $\tan (\cos^{-1} \dfrac{8}{17})$ = $\dfrac{15}{8}$

Thus, $\tan (\cos^{-1} \dfrac{8}{17})$ = $\dfrac{15}{8}$