Evaluate `cos[cos^-1 ((-sqrt(3))/2) + pi/6]`

`cos[cos^-1 ((-sqrt(3))/2) + pi/6] = cos[cos^-1(cos (5pi)/6) + pi/6]` ......`(because cos (5pi)/6 = (-sqrt(3))/2)` = `cos((5pi)/6 + pi/6)` ......`(because cos^-1 cosx = x; x ∈ [0, pi])` = `cos(pi)` = –1

Evaluate cos[cos-1(-32)+π6] - Mathematics

Question

Evaluate $\cos [\cos^{- 1} (\frac{- \sqrt{3}}{2}) + \frac{π}{6}]$

Sum

Solution

$\cos [\cos^{- 1} (\frac{- \sqrt{3}}{2}) + \frac{π}{6}] = \cos [\cos^{- 1} (\cos \frac{5 π}{6}) + \frac{π}{6}]$ ...... $(∵ \cos \frac{5 π}{6} = \frac{- \sqrt{3}}{2})$

= $\cos (\frac{5 π}{6} + \frac{π}{6})$ ...... $(∵ \cos^{- 1} \cos x = x; x \in [0, π])$

= $\cos (π)$ = –1

shaalaa.com

Properties of Inverse Trigonometric Functions

Is there an error in this question or solution?

Q 2 Q 1 Q 3

Chapter 2: Inverse Trigonometric Functions - Exercise [Page 35]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 12

Chapter 2 Inverse Trigonometric Functions
Exercise | Q 2 | Page 35

Video TutorialsVIEW ALL [9]

RELATED QUESTIONS

Prove that $\tan^{- 1} (\frac{6 x - 8 x^{3}}{1 - 12 x^{2}}) - \tan^{- 1} (\frac{4 x}{1 - 4 x^{2}}) = \tan^{- 1} 2 x; | 2 x | < \frac{1}{\sqrt{3}}$

Prove $2 \tan^{- 1} \frac{1}{2} + \tan^{- 1} \frac{1}{7} = \tan^{- 1} \frac{31}{17}$

Write the function in the simplest form: $\tan^{- 1} (\frac{\cos x - \sin x}{\cos x + \sin x})$ , $0 < x < π$

if $\tan^{- 1} \frac{x - 1}{x - 2} + \tan^{- 1} \frac{x + 1}{x + 2} = \frac{π}{4}$ then find the value of x.

Prove that:

$\sin^{- 1} \frac{8}{17} + \sin^{- 1} \frac{3}{5} = \tan^{- 1} \frac{77}{36}$

Prove that:

$\cos^{- 1} \frac{4}{5} + \cos^{- 1} \frac{12}{13} = \cos^{- 1} \frac{33}{65}$

sin (tan^–1 x), | x| < 1 is equal to ______.

Find: ∫ sin x · log cos x dx

Find the value of $\cot [\sin^{- 1} \frac{3}{5} + \sin^{- 1} \frac{4}{5}]$

Choose the correct alternative:

If $\sin^{- 1} x + \cot^{- 1} (\frac{1}{2}) = \frac{π}{2}$ , then x is equal to

Choose the correct alternative:

sin(tan^–1x), |x| < 1 is equal to

Evaluate: $\sin^{- 1} [\cos (\frac{\sin^{- 1} \sqrt{3}}{2})]$

If 3 tan^–1x + cot^–1x = π, then x equals ______.

If $\sin^{- 1} (\frac{2 a}{1 + a^{2}}) + \cos^{- 1} (\frac{1 - a^{2}}{1 + a^{2}}) = \tan^{- 1} (\frac{2 x}{1 - x^{2}})$ . where a, x ∈ ] 0, 1, then the value of x is ______.

If cos^–1x > sin^–1x, then ______.

The value of the expression tan $(\frac{1}{2} {cos}^{- 1} \frac{2}{\sqrt{3}})$

$cos (2 {tan}^{- 1} \frac{1}{7}) - sin (4 {sin}^{- 1} \frac{1}{3}) =$ ____________.

If ${tan}^{- 1} (\frac{x - 1}{x + 2}) + {tan}^{- 1} (\frac{x + 1}{x + 2}) = \frac{π}{4},$ then x is equal to ____________.

If ${tan}^{- 1} 2 {x + tan}^{- 1} 3 x = \frac{π}{4}$ , then x is ____________.

${sin}^{- 1} (1 - x) - 2 {sin}^{- 1} x = \frac{π}{2}$

${cos}^{- 1} \frac{1}{2} + 2 {sin}^{- 1} \frac{1}{2}$ is equal to ____________.

$\tan^{- 1} \frac{1}{2} + \tan^{- 1} \frac{2}{11}$ is equal to

Find the value of $\cos^{- 1} (\frac{1}{2}) + 2 \sin^{- 1} (\frac{1}{2}) \to$ :-

$50 \tan (3 \tan^{- 1} (\frac{1}{2}) + 2 \cos^{- 1} (\frac{1}{\sqrt{5}})) + 4 \sqrt{2} \tan (\frac{1}{2} \tan^{- 1} (2 \sqrt{2}))$ is equal to ______.

The value of cosec $[\sin^{- 1} (\frac{- 1}{2})] - \sec [\cos^{- 1} (\frac{- 1}{2})]$ is equal to ______.

Solve:

sin^–1(x) + sin^–1(1 – x) = cos^–1x.

Evaluate cos[cos-1(-32)+π6] - Mathematics

Advertisements

Advertisements

Question

Solution

APPEARS IN

Video TutorialsVIEW ALL [9]

RELATED QUESTIONS

Select a course

Evaluate cos[cos-1(-32)+π6] - Mathematics

Advertisements

Advertisements

Question

SolutionShow Solution

APPEARS IN

Video TutorialsVIEW ALL [9]

RELATED QUESTIONS

Select a course

Solution