Question

Please Help! Locks in 1 hour! Will give Brainlest!

Answer 1

Answer:

Last option is the correct answer

$\huge{\pink{\boxed{\frac{5\pi}{6},\:\frac{7\pi}{6}}}}$

Step-by-step explanation:

Formulae to be used:

$\blue{\boxed{\bold{\cos(\pi-\theta)=-\cos\theta}}}\\\red{\boxed{\bold{cos(\pi+\theta)=-\cos\theta}}}$

Solution:

$Let\: \theta = cos^{-1}\bigg(-\frac{\sqrt 3}{2}\bigg)$

$\implies\cos \theta = -\frac{\sqrt 3}{2}$

$\implies\cos \theta =\cos\bigg(\pi-\frac{\pi}{6}\bigg)$

$\implies\cos \theta =\cos\bigg(\frac{6\pi-\pi}{6}\bigg)$

$\huge{\red{\boxed{\implies \theta =\frac{5\pi}{6}}}}$

Further:

$Let\: \theta = cos^{-1}\bigg(-\frac{\sqrt 3}{2}\bigg)$

$\implies\cos \theta = -\frac{\sqrt 3}{2}$

$\implies\cos \theta =\cos\bigg(\pi+\frac{\pi}{6}\bigg)$

$\implies\cos \theta =\cos\bigg(\frac{6\pi+\pi}{6}\bigg)$

$\huge{\orange{\boxed{\implies \theta =\frac{7\pi}{6}}}}$

Finally:

$\huge{\purple{\boxed{ \theta =\frac{5\pi}{6},\:\frac{7\pi}{6}}}}$