Advertisements
Advertisements
प्रश्न
Prove the following result:
`tan^-1 1/7+tan^-1 1/13=tan^-1 2/9`
उत्तर
LHS = `tan^-1 1/7+tan^-1 1/13`
`=tan^-1((1/7+1/13)/(1-1/7xx1/13))` `[becausetan^-1x+tan^-1y=tan^-1((x+y)/(1-xy))`
`=tan^-1((20/91)/(90/91))`
`=tan^-1 2/9=` RHS
APPEARS IN
संबंधित प्रश्न
Solve the equation for x:sin−1x+sin−1(1−x)=cos−1x
If (tan−1x)2 + (cot−1x)2 = 5π2/8, then find x.
Find the domain of `f(x)=cos^-1x+cosx.`
Find the principal values of the following:
`cos^-1(-sqrt3/2)`
`sin^-1(sin (13pi)/7)`
Evaluate the following:
`cos^-1(cos12)`
Evaluate the following:
`tan^-1(tan (6pi)/7)`
Evaluate the following:
`sec^-1{sec (-(7pi)/3)}`
Evaluate the following:
`cosec^-1(cosec (6pi)/5)`
Evaluate the following:
`cot^-1(cot (19pi)/6)`
Evaluate the following:
`cot^-1{cot ((21pi)/4)}`
Evaluate the following:
`cos(tan^-1 24/7)`
Prove the following result-
`tan^-1 63/16 = sin^-1 5/13 + cos^-1 3/5`
Evaluate:
`cos{sin^-1(-7/25)}`
Evaluate:
`cot(sin^-1 3/4+sec^-1 4/3)`
If `sin^-1x+sin^-1y=pi/3` and `cos^-1x-cos^-1y=pi/6`, find the values of x and y.
`sin(sin^-1 1/5+cos^-1x)=1`
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))`
Solve `cos^-1sqrt3x+cos^-1x=pi/2`
Prove that: `cos^-1 4/5+cos^-1 12/13=cos^-1 33/65`
`sin^-1 4/5+2tan^-1 1/3=pi/2`
`4tan^-1 1/5-tan^-1 1/239=pi/4`
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)`
Prove that
`sin{tan^-1 (1-x^2)/(2x)+cos^-1 (1-x^2)/(2x)}=1`
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.
Write the value of tan−1 x + tan−1 `(1/x)` for x < 0.
Write the value of
\[\cos^{- 1} \left( \frac{1}{2} \right) + 2 \sin^{- 1} \left( \frac{1}{2} \right)\].
What is the principal value of `sin^-1(-sqrt3/2)?`
Write the principal value of `sin^-1(-1/2)`
Write the principal value of `tan^-1sqrt3+cot^-1sqrt3`
Write the value of \[\cos\left( \sin^{- 1} x + \cos^{- 1} x \right), \left| x \right| \leq 1\]
Write the principal value of \[\sin^{- 1} \left\{ \cos\left( \sin^{- 1} \frac{1}{2} \right) \right\}\]
The number of solutions of the equation \[\tan^{- 1} 2x + \tan^{- 1} 3x = \frac{\pi}{4}\] is
Let f (x) = `e^(cos^-1){sin(x+pi/3}.`
Then, f (8π/9) =
If tan−1 3 + tan−1 x = tan−1 8, then x =
The value of \[\sin\left( 2\left( \tan^{- 1} 0 . 75 \right) \right)\] is equal to
Find : \[\int\frac{2 \cos x}{\left( 1 - \sin x \right) \left( 1 + \sin^2 x \right)}dx\] .
Find the value of `sin^-1(cos((33π)/5))`.
