Advertisements
Advertisements
प्रश्न
`4tan^-1 1/5-tan^-1 1/239=pi/4`
उत्तर
LHS = `4tan^-1 1/5-tan^-1 1/239`
`=2tan^-1{(2xx1/5)/(1-(1/5)^2)}-tan^-1 1/239` `[because2tan^-1x=tan^-1{(2x)/(1-x^2)}]`
`=2tan^-1{(2/5)/(24/25)}-tan^-1 1/239`
`=2tan^-1 5/12-tan^-1 1/239`
`=tan^-1{(2xx5/12)/(1-(5/12)^2)}-tan^-1 1/239` `[because2tan^-1x=tan^-1{(2x)/(1-x^2)}]`
`=tan^-1{(5/6)/(119/144)}-tan^-1 1/239`
`=tan^-1 120/119-tan^-1 1/239`
`=tan^-1((120/119-17/239)/(1+120/119xx1/239))` `[becausetan^-1x-tan^-1y=tan^-1((x-y)/(1+xy))]`
`=tan^-1 1=pi/4=`RHS
APPEARS IN
संबंधित प्रश्न
Prove that :
`2 tan^-1 (sqrt((a-b)/(a+b))tan(x/2))=cos^-1 ((a cos x+b)/(a+b cosx))`
If sin [cot−1 (x+1)] = cos(tan−1x), then find x.
Find the principal values of the following:
`cos^-1(tan (3pi)/4)`
`sin^-1(sin (17pi)/8)`
`sin^-1(sin3)`
Evaluate the following:
`cos^-1{cos(-pi/4)}`
Evaluate the following:
`cos^-1(cos3)`
Evaluate the following:
`sec^-1(sec (2pi)/3)`
Evaluate the following:
`sec^-1(sec (25pi)/6)`
Evaluate the following:
`cosec^-1(cosec (3pi)/4)`
Evaluate the following:
`cot^-1(cot (19pi)/6)`
Write the following in the simplest form:
`cot^-1 a/sqrt(x^2-a^2),| x | > a`
Write the following in the simplest form:
`tan^-1(x/(a+sqrt(a^2-x^2))),-a<x<a`
Prove the following result
`tan(cos^-1 4/5+tan^-1 2/3)=17/6`
Prove the following result-
`tan^-1 63/16 = sin^-1 5/13 + cos^-1 3/5`
Evaluate:
`cos{sin^-1(-7/25)}`
Find the value of `tan^-1 (x/y)-tan^-1((x-y)/(x+y))`
`tan^-1 2/3=1/2tan^-1 12/5`
`tan^-1 1/7+2tan^-1 1/3=pi/4`
Solve the following equation for x:
`tan^-1((2x)/(1-x^2))+cot^-1((1-x^2)/(2x))=(2pi)/3,x>0`
Write the value of tan−1x + tan−1 `(1/x)`for x > 0.
What is the value of cos−1 `(cos (2x)/3)+sin^-1(sin (2x)/3)?`
Write the value of sin (cot−1 x).
Write the value of sin−1
\[\left( \sin( -{600}°) \right)\].
Write the value of cos \[\left( 2 \sin^{- 1} \frac{1}{2} \right)\]
Write the value of sin−1 \[\left( \cos\frac{\pi}{9} \right)\]
Write the value of cos−1 \[\left( \cos\frac{5\pi}{4} \right)\]
If 4 sin−1 x + cos−1 x = π, then what is the value of x?
Write the value of \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
Write the value of \[\tan^{- 1} \left( \frac{1}{x} \right)\] for x < 0 in terms of `cot^-1x`
If \[\cos\left( \sin^{- 1} \frac{2}{5} + \cos^{- 1} x \right) = 0\], find the value of x.
Find the value of \[\cos^{- 1} \left( \cos\frac{13\pi}{6} \right)\]
The number of solutions of the equation \[\tan^{- 1} 2x + \tan^{- 1} 3x = \frac{\pi}{4}\] is
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
If \[\cos^{- 1} x > \sin^{- 1} x\], then
The value of sin \[\left( \frac{1}{4} \sin^{- 1} \frac{\sqrt{63}}{8} \right)\] is
Prove that : \[\cot^{- 1} \frac{\sqrt{1 + \sin x} + \sqrt{1 - \sin x}}{\sqrt{1 + \sin x} - \sqrt{1 - \sin x}} = \frac{x}{2}, 0 < x < \frac{\pi}{2}\] .
