Question

i need the answer plz help me​

Answer 1

Answer:

Step-by-step explanation:

We have,

$\tt{cos\left\{cos^{-1}\left(\dfrac{1}{6}\right)+sin^{-1}\left(\dfrac{1}{6}\right)\right\}+cos\left[cos^{-1}\left\{cos\left(\dfrac{5\pi}{6}\right)\right\}\right]}$

$\sf{=cos\left(\dfrac{\pi}{2}\right)+cos\left[cos^{-1}\left\{cos\left(\pi-\dfrac{\pi}{6}\right)\right\}\right]}$

$\sf{=cos\left(\dfrac{\pi}{2}\right)+cos\left[cos^{-1}\left\{-cos\left(\dfrac{\pi}{6}\right)\right\}\right]}$

$\sf{=cos\left(\dfrac{\pi}{2}\right)+cos\left[cos^{-1}\left(-\dfrac{\sqrt{3}}{2}\right)\right]}$

$\sf{=cos\left(\dfrac{\pi}{2}\right)+cos\left[\pi-cos^{-1}\left(\dfrac{\sqrt{3}}{2}\right)\right]}$

$\sf{=cos\left(\dfrac{\pi}{2}\right)+cos\left(\pi-\dfrac{\pi}{6}\right)}$

$\sf{=cos\left(\dfrac{\pi}{2}\right)-cos\left(\dfrac{\pi}{6}\right)}$

$\sf{=0-\dfrac{\sqrt{3}}{2}}$

$\sf{=-\dfrac{\sqrt{3}}{2}}$