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cos cos^-1 [-root3/2] +pi/4]

$\cos [\cos^{- 1} (\frac{- \sqrt{3}}{2}) + \frac{π}{4}] L e t θ = \cos^{- 1} (\frac{- \sqrt{3}}{2}) \Rightarrow \cos θ = \frac{- \sqrt{3}}{2} \Rightarrow \cos θ = \cos \frac{5 π}{6} ∴ \cos [\cos^{- 1} (\frac{- \sqrt{3}}{2}) + \frac{π}{4}] = \cos (\frac{5 π}{6} + \frac{π}{4}) = \cos \frac{5 π}{6} . \cos \frac{π}{4} - \sin \frac{5 π}{6} . \sin \frac{π}{4} [\cos (A + B) = \cos A \cos B - \sin A \sin B] = \cos \frac{5 π}{6} . (\frac{1}{\sqrt{2}}) - \sin \frac{5 π}{6} . (\frac{1}{\sqrt{2}}) = \frac{1}{\sqrt{2}} [\cos \frac{5 π}{6} - \sin \frac{5 π}{6}] = \frac{1}{\sqrt{2}} [\frac{- \sqrt{3}}{2} - \frac{1}{2}] = \frac{1}{\sqrt{2}} [\frac{- \sqrt{3} - 1}{2}]$

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