Advertisements
Advertisements
Question
Evaluate the following:
`tan^-1(tan2)`
Advertisements
Solution
We know that
`tan^-1(tantheta)=theta, -pi/2<theta<pi/2`
We have
`tan^-1(tan2)=tan^-1[tan(-pi+2)]`
= 2 - π
APPEARS IN
RELATED QUESTIONS
Solve the equation for x:sin−1x+sin−1(1−x)=cos−1x
Solve for x:
`2tan^(-1)(cosx)=tan^(-1)(2"cosec" x)`
Evaluate the following:
`cos^-1(cos4)`
Evaluate the following:
`cos^-1(cos12)`
Evaluate the following:
`sec^-1(sec (9pi)/5)`
Write the following in the simplest form:
`tan^-1{x+sqrt(1+x^2)},x in R `
Evaluate:
`cosec{cot^-1(-12/5)}`
Evaluate:
`cot(tan^-1a+cot^-1a)`
If `cos^-1x + cos^-1y =pi/4,` find the value of `sin^-1x+sin^-1y`
`5tan^-1x+3cot^-1x=2x`
Prove the following result:
`tan^-1 1/4+tan^-1 2/9=sin^-1 1/sqrt5`
Solve the following equation for x:
tan−1(x −1) + tan−1x tan−1(x + 1) = tan−13x
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:
cot−1x − cot−1(x + 2) =`pi/12`, x > 0
Evaluate: `cos(sin^-1 3/5+sin^-1 5/13)`
`sin^-1 63/65=sin^-1 5/13+cos^-1 3/5`
`(9pi)/8-9/4sin^-1 1/3=9/4sin^-1 (2sqrt2)/3`
Solve the equation `cos^-1 a/x-cos^-1 b/x=cos^-1 1/b-cos^-1 1/a`
Solve the following equation for x:
`tan^-1 1/4+2tan^-1 1/5+tan^-1 1/6+tan^-1 1/x=pi/4`
If x > 1, then write the value of sin−1 `((2x)/(1+x^2))` in terms of tan−1 x.
Write the value of tan−1x + tan−1 `(1/x)`for x > 0.
Write the value of sin (cot−1 x).
Write the value of
\[\cos^{- 1} \left( \frac{1}{2} \right) + 2 \sin^{- 1} \left( \frac{1}{2} \right)\].
Write the value of cos \[\left( 2 \sin^{- 1} \frac{1}{2} \right)\]
Write the value of tan−1\[\left\{ \tan\left( \frac{15\pi}{4} \right) \right\}\]
What is the principal value of `sin^-1(-sqrt3/2)?`
Write the value of \[\tan^{- 1} \left\{ 2\sin\left( 2 \cos^{- 1} \frac{\sqrt{3}}{2} \right) \right\}\]
Find the value of \[2 \sec^{- 1} 2 + \sin^{- 1} \left( \frac{1}{2} \right)\]
Find the value of \[\tan^{- 1} \left( \tan\frac{9\pi}{8} \right)\]
\[\text{ If } u = \cot^{- 1} \sqrt{\tan \theta} - \tan^{- 1} \sqrt{\tan \theta}\text{ then }, \tan\left( \frac{\pi}{4} - \frac{u}{2} \right) =\]
If 4 cos−1 x + sin−1 x = π, then the value of x is
In a ∆ ABC, if C is a right angle, then
\[\tan^{- 1} \left( \frac{a}{b + c} \right) + \tan^{- 1} \left( \frac{b}{c + a} \right) =\]
The value of sin \[\left( \frac{1}{4} \sin^{- 1} \frac{\sqrt{63}}{8} \right)\] is
\[\cot\left( \frac{\pi}{4} - 2 \cot^{- 1} 3 \right) =\]
Find the domain of `sec^(-1) x-tan^(-1)x`
tanx is periodic with period ____________.
The value of tan `("cos"^-1 4/5 + "tan"^-1 2/3) =`
Find the value of `sin^-1(cos((33π)/5))`.
