Question

the value of cos(sin-1 8/17) is​

Answer 1

Step-by-step explanation:

0.999...48

that's answer

Answer 2

Answer:

Step-by-step explanation:

We have,

$\rm{cos\left(sin^{-1}\left(\dfrac{8}{17}\right)\right)}$

We know,

$\boxed{\rm{sin^{-1}(x)=cos^{-1}\left(\sqrt{1-{x}^{2}}\right)}}$

So,

$\rm{=cos\left\{cos^{-1}\left(\sqrt{1-\left(\dfrac{8}{17}\right)^2}\right)\right\}}$

$\rm{=cos\left\{cos^{-1}\left(\sqrt{1-\dfrac{64}{289}}\right)\right\}}$

$\rm{=cos\left\{cos^{-1}\left(\sqrt{\dfrac{289-64}{289}}\right)\right\}}$

$\rm{=cos\left\{cos^{-1}\left(\sqrt{\dfrac{225}{289}}\right)\right\}}$

$\rm{=cos\left\{cos^{-1}\left(\dfrac{15}{17}\right)\right\}}$

$\bf{Since\,\,\,\,cos\big(cos^{-1}(x)\big)=x\,,\,\,\,so\,,}$

$\rm{=\dfrac{15}{17}}$