Advertisements
Advertisements
Question
`2tan^-1 3/4-tan^-1 17/31=pi/4`
Advertisements
Solution
LHS = `2tan^-1 3/4-tan^-1 17/31`
`=tan^-1{(2xx3/4)/(1-(3/4)^2)}-tan^-1 17/31` `[because2tan^-1x=tan^-1{(2x)/(1-x^2)}]`
`=tan^-1{(3/2)/(7/16)}-tan^-1 17/31`
`=tan^-1 24/7-tan^-1 17/31`
`=tan^-1((24/7-17/31)/(1+24/7xx17/31))` `[becausetan^-1x-tan^-1y=tan^-1((x-y)/(1+xy))]`
`=tan^-1((625/217)/(625/217))`
`=tan^-1 1=pi/4=` RHS
APPEARS IN
RELATED QUESTIONS
Solve the following for x :
`tan^(-1)((x-2)/(x-3))+tan^(-1)((x+2)/(x+3))=pi/4,|x|<1`
Find the principal values of the following:
`cos^-1(-sqrt3/2)`
`sin^-1(sin (13pi)/7)`
Evaluate the following:
`cos^-1{cos (13pi)/6}`
Evaluate the following:
`cos^-1(cos5)`
Evaluate the following:
`cot^-1(cot (19pi)/6)`
Evaluate the following:
`cot^-1{cot ((21pi)/4)}`
Write the following in the simplest form:
`tan^-1{(sqrt(1+x^2)-1)/x},x !=0`
Prove the following result
`tan(cos^-1 4/5+tan^-1 2/3)=17/6`
Evaluate:
`cos(tan^-1 3/4)`
`tan^-1x+2cot^-1x=(2x)/3`
Solve the following equation for x:
`2tan^-1(sinx)=tan^-1(2sinx),x!=pi/2`
Solve the following equation for x:
`tan^-1((x-2)/(x-1))+tan^-1((x+2)/(x+1))=pi/4`
For any a, b, x, y > 0, prove that:
`2/3tan^-1((3ab^2-a^3)/(b^3-3a^2b))+2/3tan^-1((3xy^2-x^3)/(y^3-3x^2y))=tan^-1 (2alphabeta)/(alpha^2-beta^2)`
`where alpha =-ax+by, beta=bx+ay`
If `sin^-1x+sin^-1y+sin^-1z=(3pi)/2,` then write the value of x + y + z.
If x < 0, then write the value of cos−1 `((1-x^2)/(1+x^2))` in terms of tan−1 x.
If −1 < x < 0, then write the value of `sin^-1((2x)/(1+x^2))+cos^-1((1-x^2)/(1+x^2))`
Write the value of \[\tan^{- 1} \frac{a}{b} - \tan^{- 1} \left( \frac{a - b}{a + b} \right)\]
What is the principal value of `sin^-1(-sqrt3/2)?`
Write the value of \[\tan\left( 2 \tan^{- 1} \frac{1}{5} \right)\]
Write the value of \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
2 tan−1 {cosec (tan−1 x) − tan (cot−1 x)} is equal to
If \[\cos^{- 1} \frac{x}{a} + \cos^{- 1} \frac{y}{b} = \alpha, then\frac{x^2}{a^2} - \frac{2xy}{ab}\cos \alpha + \frac{y^2}{b^2} = \]
If sin−1 x − cos−1 x = `pi/6` , then x =
The number of solutions of the equation \[\tan^{- 1} 2x + \tan^{- 1} 3x = \frac{\pi}{4}\] is
If x < 0, y < 0 such that xy = 1, then tan−1 x + tan−1 y equals
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
The value of \[\tan\left( \cos^{- 1} \frac{3}{5} + \tan^{- 1} \frac{1}{4} \right)\]
If y = sin (sin x), prove that \[\frac{d^2 y}{d x^2} + \tan x \frac{dy}{dx} + y \cos^2 x = 0 .\]
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)`.
Solve for x : {xcos(cot-1 x) + sin(cot-1 x)}2 = `51/50`
Find the value of `sin^-1(cos((33π)/5))`.
