Advertisements
Advertisements
प्रश्न
Write the value of \[\tan\left( 2 \tan^{- 1} \frac{1}{5} \right)\]
उत्तर
\[\tan\left( 2 \tan^{- 1} \frac{1}{5} \right) = \tan\left[ \tan^{- 1} \frac{2 \times \frac{1}{5}}{1 - \left( \frac{1}{5} \right)^2} \right]\]
\[ = \tan\left( \tan^{- 1} \frac{\frac{2}{5}}{\frac{24}{25}} \right)\]
\[ = \tan\left( \tan^{- 1} \frac{5}{12} \right)\]
\[ = \frac{5}{12}\]
APPEARS IN
संबंधित प्रश्न
Solve the following for x :
`tan^(-1)((x-2)/(x-3))+tan^(-1)((x+2)/(x+3))=pi/4,|x|<1`
Solve the following for x:
`sin^(-1)(1-x)-2sin^-1 x=pi/2`
If `tan^(-1)((x-2)/(x-4)) +tan^(-1)((x+2)/(x+4))=pi/4` ,find the value of x
Find the principal values of the following:
`cos^-1(-sqrt3/2)`
Find the principal values of the following:
`cos^-1(tan (3pi)/4)`
`sin^-1(sin (5pi)/6)`
`sin^-1(sin12)`
Evaluate the following:
`cos^-1(cos12)`
Evaluate the following:
`tan^-1(tan (6pi)/7)`
Evaluate the following:
`sec^-1(sec pi/3)`
Write the following in the simplest form:
`tan^-1{x+sqrt(1+x^2)},x in R `
Write the following in the simplest form:
`tan^-1{(sqrt(1+x^2)-1)/x},x !=0`
Write the following in the simplest form:
`tan^-1sqrt((a-x)/(a+x)),-a<x<a`
Evaluate the following:
`sin(sin^-1 7/25)`
Evaluate the following:
`sec(sin^-1 12/13)`
Prove the following result-
`tan^-1 63/16 = sin^-1 5/13 + cos^-1 3/5`
Prove the following result
`sin(cos^-1 3/5+sin^-1 5/13)=63/65`
Evaluate:
`cot(sin^-1 3/4+sec^-1 4/3)`
Evaluate:
`sin(tan^-1x+tan^-1 1/x)` for x < 0
If `sin^-1x+sin^-1y=pi/3` and `cos^-1x-cos^-1y=pi/6`, find the values of x and y.
`5tan^-1x+3cot^-1x=2x`
Solve the following equation for x:
tan−1`((1-x)/(1+x))-1/2` tan−1x = 0, where x > 0
`2tan^-1 1/5+tan^-1 1/8=tan^-1 4/7`
If `sin^-1 (2a)/(1+a^2)-cos^-1 (1-b^2)/(1+b^2)=tan^-1 (2x)/(1-x^2)`, then prove that `x=(a-b)/(1+ab)`
If `sin^-1 (2a)/(1+a^2)+sin^-1 (2b)/(1+b^2)=2tan^-1x,` Prove that `x=(a+b)/(1-ab).`
Write the range of tan−1 x.
Write the value of sin \[\left\{ \frac{\pi}{3} - \sin^{- 1} \left( - \frac{1}{2} \right) \right\}\]
The value of tan \[\left\{ \cos^{- 1} \frac{1}{5\sqrt{2}} - \sin^{- 1} \frac{4}{\sqrt{17}} \right\}\] is
2 tan−1 {cosec (tan−1 x) − tan (cot−1 x)} is equal to
\[\tan^{- 1} \frac{1}{11} + \tan^{- 1} \frac{2}{11}\] is equal to
If tan−1 3 + tan−1 x = tan−1 8, then x =
The value of \[\sin^{- 1} \left( \cos\frac{33\pi}{5} \right)\] is
It \[\tan^{- 1} \frac{x + 1}{x - 1} + \tan^{- 1} \frac{x - 1}{x} = \tan^{- 1}\] (−7), then the value of x is
In a ∆ ABC, if C is a right angle, then
\[\tan^{- 1} \left( \frac{a}{b + c} \right) + \tan^{- 1} \left( \frac{b}{c + a} \right) =\]
If tan−1 (cot θ) = 2 θ, then θ =
Prove that : \[\cot^{- 1} \frac{\sqrt{1 + \sin x} + \sqrt{1 - \sin x}}{\sqrt{1 + \sin x} - \sqrt{1 - \sin x}} = \frac{x}{2}, 0 < x < \frac{\pi}{2}\] .
Find the domain of `sec^(-1)(3x-1)`.
Find the simplified form of `cos^-1 (3/5 cosx + 4/5 sin x)`, where x ∈ `[(-3pi)/4, pi/4]`
tanx is periodic with period ____________.
