Advertisements
Advertisements
प्रश्न
Write the principal value of `tan^-1sqrt3+cot^-1sqrt3`
उत्तर
We know
\[\tan^{- 1} x + \cot^{- 1} x = \frac{\pi}{2}\]
\[\therefore \tan^{- 1} \sqrt{3} + \cot^{- 1} \sqrt{3} = \frac{\pi}{2}\]
APPEARS IN
संबंधित प्रश्न
Solve the equation for x:sin−1x+sin−1(1−x)=cos−1x
If sin [cot−1 (x+1)] = cos(tan−1x), then find x.
If (tan−1x)2 + (cot−1x)2 = 5π2/8, then find x.
Find the principal values of the following:
`cos^-1(-1/sqrt2)`
Evaluate the following:
`cos^-1(cos3)`
Evaluate the following:
`cos^-1(cos5)`
Evaluate the following:
`sec^-1(sec pi/3)`
Evaluate the following:
`cosec^-1(cosec (13pi)/6)`
Evaluate the following:
`tan(cos^-1 8/17)`
Evaluate:
`cos{sin^-1(-7/25)}`
Evaluate:
`cosec{cot^-1(-12/5)}`
Evaluate:
`cot(sin^-1 3/4+sec^-1 4/3)`
`tan^-1x+2cot^-1x=(2x)/3`
Prove the following result:
`sin^-1 12/13+cos^-1 4/5+tan^-1 63/16=pi`
Sum the following series:
`tan^-1 1/3+tan^-1 2/9+tan^-1 4/33+...+tan^-1 (2^(n-1))/(1+2^(2n-1))`
`(9pi)/8-9/4sin^-1 1/3=9/4sin^-1 (2sqrt2)/3`
Prove that:
`2sin^-1 3/5=tan^-1 24/7`
`sin^-1 4/5+2tan^-1 1/3=pi/2`
If `sin^-1 (2a)/(1+a^2)+sin^-1 (2b)/(1+b^2)=2tan^-1x,` Prove that `x=(a+b)/(1-ab).`
Solve the following equation for x:
`3sin^-1 (2x)/(1+x^2)-4cos^-1 (1-x^2)/(1+x^2)+2tan^-1 (2x)/(1-x^2)=pi/3`
Write the value of tan−1x + tan−1 `(1/x)`for x > 0.
If \[\tan^{- 1} (\sqrt{3}) + \cot^{- 1} x = \frac{\pi}{2},\] find x.
If 4 sin−1 x + cos−1 x = π, then what is the value of x?
What is the principal value of `sin^-1(-sqrt3/2)?`
Write the value of \[\cos\left( \sin^{- 1} x + \cos^{- 1} x \right), \left| x \right| \leq 1\]
Write the principal value of \[\sin^{- 1} \left\{ \cos\left( \sin^{- 1} \frac{1}{2} \right) \right\}\]
\[\text{ If } u = \cot^{- 1} \sqrt{\tan \theta} - \tan^{- 1} \sqrt{\tan \theta}\text{ then }, \tan\left( \frac{\pi}{4} - \frac{u}{2} \right) =\]
\[\text{ If }\cos^{- 1} \frac{x}{3} + \cos^{- 1} \frac{y}{2} = \frac{\theta}{2}, \text{ then }4 x^2 - 12xy \cos\frac{\theta}{2} + 9 y^2 =\]
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
It \[\tan^{- 1} \frac{x + 1}{x - 1} + \tan^{- 1} \frac{x - 1}{x} = \tan^{- 1}\] (−7), then the value of x is
Prove that : \[\tan^{- 1} \left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) = \frac{\pi}{4} + \frac{1}{2} \cos^{- 1} x^2 ; 1 < x < 1\].
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.
Write the value of \[\cos^{- 1} \left( - \frac{1}{2} \right) + 2 \sin^{- 1} \left( \frac{1}{2} \right)\] .
tanx is periodic with period ____________.
The period of the function f(x) = tan3x is ____________.
The value of sin `["cos"^-1 (7/25)]` is ____________.