Question

Value of cos[π/6 + cos⁻¹(- 1/2)] is.....,Select Proper option from the given options.
(a) - √3/2
(b) √3-1/2√2
(c) √5-1/4
(d) √3+1/2√2

Answer 1

we have to find the value of cos[π/6 + cos^-1(-1/2)]

we know, cos^-1(-x) = π - cos^-1x

so, cos[π/6 + cos^-1(-1/2)] = cos[π/6 + π - cos^-1(1/2)]

= cos[π/6 + π - π/3 ] because cos^-1(1/2) = π/3

= cos [π + π/6 ]

= - cos(π/6)

= -√3/2

hence, option (a) is correct

Answer 2

Dear Student,

Answer:Option a is correct (-√3/2) is the answer

Solution:

${cos}^{ - 1} ( - x) = \pi - {cos}^{ - 1} x \\ \\ \cos(( \frac{\pi}{6} ) + \pi - {cos}^{ - 1} ( \frac{1}{2} )) \\ \\ = \cos(( \frac{\pi}{6} ) + \pi - {cos}^{ - 1} ( cos \frac{\pi}{3} )) \\ \\ = \cos( \frac{\pi}{6} + \pi - \frac{\pi}{3} )) \\ \\ = cos( \frac{\pi + 6\pi - 2\pi}{6} ) \\ = cos( \frac{5\pi}{6} ) \\ \\ = cos(\pi - \frac{\pi}{6} ) \\ = - cos( \frac{\pi}{6} ) \\ \\ = - \frac{ \sqrt{3} }{2}$
Hope it helps you