Advertisements
Advertisements
Question
The value of \[\sin^{- 1} \left( \cos\frac{33\pi}{5} \right)\] is
Options
`(3pi)/5`
`-pi/10`
`pi/10`
`(7pi)/5`
Advertisements
Solution
(b) `-pi/10`
\[\sin^{- 1} \left( \cos\frac{33\pi}{5} \right) = \sin^{- 1} \left\{ \cos\left( 6\pi + \frac{3\pi}{5} \right) \right\}\]
\[ = \sin^{- 1} \left\{ \cos\left( \frac{3\pi}{5} \right) \right\}\]
\[ = \sin^{- 1} \left\{ \sin\left( \frac{\pi}{2} - \frac{3\pi}{5} \right) \right\}\]
\[ = \frac{\pi}{2} - \frac{3\pi}{5}\]
\[ = - \frac{\pi}{10}\]
\[\]
APPEARS IN
RELATED QUESTIONS
Solve the equation for x:sin−1x+sin−1(1−x)=cos−1x
Solve the following for x:
`sin^(-1)(1-x)-2sin^-1 x=pi/2`
If (tan−1x)2 + (cot−1x)2 = 5π2/8, then find x.
If `tan^(-1)((x-2)/(x-4)) +tan^(-1)((x+2)/(x+4))=pi/4` ,find the value of x
Find the domain of `f(x)=cos^-1x+cosx.`
`sin^-1(sin pi/6)`
Evaluate the following:
`cos^-1{cos (5pi)/4}`
Evaluate the following:
`cos^-1{cos (13pi)/6}`
Evaluate the following:
`tan^-1(tan pi/3)`
Evaluate the following:
`tan^-1(tan12)`
Evaluate the following:
`sec^-1{sec (-(7pi)/3)}`
Evaluate the following:
`cot^-1(cot (19pi)/6)`
Write the following in the simplest form:
`sin{2tan^-1sqrt((1-x)/(1+x))}`
Prove the following result-
`tan^-1 63/16 = sin^-1 5/13 + cos^-1 3/5`
Evaluate:
`cosec{cot^-1(-12/5)}`
Evaluate: `sin{cos^-1(-3/5)+cot^-1(-5/12)}`
Evaluate:
`cot(sin^-1 3/4+sec^-1 4/3)`
Prove the following result:
`tan^-1 1/7+tan^-1 1/13=tan^-1 2/9`
Solve the following equation for x:
`tan^-1(2+x)+tan^-1(2-x)=tan^-1 2/3, where x< -sqrt3 or, x>sqrt3`
`sin^-1 63/65=sin^-1 5/13+cos^-1 3/5`
`sin^-1 5/13+cos^-1 3/5=tan^-1 63/16`
Prove that: `cos^-1 4/5+cos^-1 12/13=cos^-1 33/65`
`2tan^-1(1/2)+tan^-1(1/7)=tan^-1(31/17)`
Solve the following equation for x:
`tan^-1 1/4+2tan^-1 1/5+tan^-1 1/6+tan^-1 1/x=pi/4`
Write the value of `sin^-1((-sqrt3)/2)+cos^-1((-1)/2)`
Write the difference between maximum and minimum values of sin−1 x for x ∈ [− 1, 1].
Write the value of sin (cot−1 x).
Write the value of cos\[\left( 2 \sin^{- 1} \frac{1}{3} \right)\]
Write the value of cos \[\left( 2 \sin^{- 1} \frac{1}{2} \right)\]
Write the value of sin \[\left\{ \frac{\pi}{3} - \sin^{- 1} \left( - \frac{1}{2} \right) \right\}\]
If 4 sin−1 x + cos−1 x = π, then what is the value of x?
Write the value of \[\tan^{- 1} \left\{ 2\sin\left( 2 \cos^{- 1} \frac{\sqrt{3}}{2} \right) \right\}\]
Write the value of \[\cos\left( \sin^{- 1} x + \cos^{- 1} x \right), \left| x \right| \leq 1\]
Write the principal value of \[\sin^{- 1} \left\{ \cos\left( \sin^{- 1} \frac{1}{2} \right) \right\}\]
If \[\cos\left( \sin^{- 1} \frac{2}{5} + \cos^{- 1} x \right) = 0\], find the value of x.
If \[3\sin^{- 1} \left( \frac{2x}{1 + x^2} \right) - 4 \cos^{- 1} \left( \frac{1 - x^2}{1 + x^2} \right) + 2 \tan^{- 1} \left( \frac{2x}{1 - x^2} \right) = \frac{\pi}{3}\] is equal to
\[\cot\left( \frac{\pi}{4} - 2 \cot^{- 1} 3 \right) =\]
If y = sin (sin x), prove that \[\frac{d^2 y}{d x^2} + \tan x \frac{dy}{dx} + y \cos^2 x = 0 .\]
The value of sin `["cos"^-1 (7/25)]` is ____________.
