Advertisements
Advertisements
Question
Write the value of `sin^-1((-sqrt3)/2)+cos^-1((-1)/2)`
Advertisements
Solution
`sin^-1(-x)=-sin^-1x,x in[-1,1]`
`cos^-1(-x)=pi-cos^-1x,x in[-1,1]`
`therefore sin^-1(-(sqrt3)/2)+cos^-1(-1/2)`
`=-sin^-1(sqrt3/2)+pi-cos^-1(1/2)`
`=-sin^-1(sin pi/3)+pi-cos^-1(cos pi/3)`
`=-pi/3+pi-pi/3`
`=pi/3`
`thereforesin^-1(-sqrt3/2)+cos^-1(-1/2)=pi/3`
APPEARS IN
RELATED QUESTIONS
`sin^-1(sin pi/6)`
`sin^-1(sin (7pi)/6)`
Evaluate the following:
`cos^-1(cos12)`
Evaluate the following:
`tan^-1(tan (7pi)/6)`
Evaluate the following:
`cosec^-1(cosec (6pi)/5)`
Evaluate the following:
`cot^-1(cot pi/3)`
Evaluate the following:
`cot^-1{cot ((21pi)/4)}`
Write the following in the simplest form:
`tan^-1{sqrt(1+x^2)-x},x in R`
Evaluate the following:
`tan(cos^-1 8/17)`
Evaluate the following:
`cos(tan^-1 24/7)`
Evaluate:
`cot{sec^-1(-13/5)}`
If `cos^-1x + cos^-1y =pi/4,` find the value of `sin^-1x+sin^-1y`
Solve the following equation for x:
`tan^-1((1-x)/(1+x))-1/2 tan^-1x` = 0, where x > 0
Solve the following equation for x:
`tan^-1(2+x)+tan^-1(2-x)=tan^-1 2/3, where x< -sqrt3 or, x>sqrt3`
Solve the following:
`sin^-1x+sin^-1 2x=pi/3`
Evaluate the following:
`tan 1/2(cos^-1 sqrt5/3)`
Evaluate the following:
`sin(2tan^-1 2/3)+cos(tan^-1sqrt3)`
If `sin^-1 (2a)/(1+a^2)+sin^-1 (2b)/(1+b^2)=2tan^-1x,` Prove that `x=(a+b)/(1-ab).`
Find the value of the following:
`tan^-1{2cos(2sin^-1 1/2)}`
Find the value of the following:
`cos(sec^-1x+\text(cosec)^-1x),` | x | ≥ 1
Solve the following equation for x:
`cos^-1((x^2-1)/(x^2+1))+1/2tan^-1((2x)/(1-x^2))=(2x)/3`
Write the difference between maximum and minimum values of sin−1 x for x ∈ [− 1, 1].
Write the value of cos \[\left( 2 \sin^{- 1} \frac{1}{2} \right)\]
Write the value of \[\tan^{- 1} \frac{a}{b} - \tan^{- 1} \left( \frac{a - b}{a + b} \right)\]
Write the value of \[\tan^{- 1} \left( \frac{1}{x} \right)\] for x < 0 in terms of `cot^-1x`
If \[\tan^{- 1} \left( \frac{\sqrt{1 + x^2} - \sqrt{1 - x^2}}{\sqrt{1 + x^2} + \sqrt{1 - x^2}} \right)\] = α, then x2 =
2 tan−1 {cosec (tan−1 x) − tan (cot−1 x)} is equal to
\[\text{ If } u = \cot^{- 1} \sqrt{\tan \theta} - \tan^{- 1} \sqrt{\tan \theta}\text{ then }, \tan\left( \frac{\pi}{4} - \frac{u}{2} \right) =\]
Let f (x) = `e^(cos^-1){sin(x+pi/3}.`
Then, f (8π/9) =
If \[\cos^{- 1} \frac{x}{2} + \cos^{- 1} \frac{y}{3} = \theta,\] then 9x2 − 12xy cos θ + 4y2 is equal to
The value of \[\cos^{- 1} \left( \cos\frac{5\pi}{3} \right) + \sin^{- 1} \left( \sin\frac{5\pi}{3} \right)\] is
It \[\tan^{- 1} \frac{x + 1}{x - 1} + \tan^{- 1} \frac{x - 1}{x} = \tan^{- 1}\] (−7), then the value of x is
The value of sin \[\left( \frac{1}{4} \sin^{- 1} \frac{\sqrt{63}}{8} \right)\] is
The value of \[\tan\left( \cos^{- 1} \frac{3}{5} + \tan^{- 1} \frac{1}{4} \right)\]
If \[\tan^{- 1} \left( \frac{1}{1 + 1 . 2} \right) + \tan^{- 1} \left( \frac{1}{1 + 2 . 3} \right) + . . . + \tan^{- 1} \left( \frac{1}{1 + n . \left( n + 1 \right)} \right) = \tan^{- 1} \theta\] , then find the value of θ.
Find the value of x, if tan `[sec^(-1) (1/x) ] = sin ( tan^(-1) 2) , x > 0 `.
Find the simplified form of `cos^-1 (3/5 cosx + 4/5 sin x)`, where x ∈ `[(-3pi)/4, pi/4]`
