Advertisements
Advertisements
प्रश्न
Prove that:
`2sin^-1 3/5=tan^-1 24/7`
उत्तर
= `2sin^-1 3/5 = 2tan^-1 3/sqrt(5^2 - 3^2)` ...`[sin^-1 "p"/"h" = tan^-1 "p"/sqrt("h"^2 - "p"^2)]`
= `2tan^-1 3/4`
= `tan^-1 (2 xx 3/4)/(1 - (3/4)^2)` ...`[2tan^-1 = tan^-1 (2x)/(1 - x^2)]`
= `tan^-1 (3/2)/(7/16)`
`= tan^-1 24/7`
APPEARS IN
संबंधित प्रश्न
Write the value of `tan(2tan^(-1)(1/5))`
Prove that :
`2 tan^-1 (sqrt((a-b)/(a+b))tan(x/2))=cos^-1 ((a cos x+b)/(a+b cosx))`
Show that:
`2 sin^-1 (3/5)-tan^-1 (17/31)=pi/4`
If (tan−1x)2 + (cot−1x)2 = 5π2/8, then find x.
If tan-1x+tan-1y=π/4,xy<1, then write the value of x+y+xy.
If a line makes angles 90° and 60° respectively with the positive directions of x and y axes, find the angle which it makes with the positive direction of z-axis.
Find the domain of `f(x)=cos^-1x+cosx.`
Find the principal values of the following:
`cos^-1(sin (4pi)/3)`
`sin^-1(sin (13pi)/7)`
`sin^-1{(sin - (17pi)/8)}`
Evaluate the following:
`tan^-1(tan (9pi)/4)`
Evaluate the following:
`cosec^-1(cosec (3pi)/4)`
Evaluate the following:
`cosec^-1(cosec (6pi)/5)`
Evaluate the following:
`cosec^-1{cosec (-(9pi)/4)}`
Evaluate the following:
`cot^-1(cot (4pi)/3)`
Write the following in the simplest form:
`tan^-1{(sqrt(1+x^2)+1)/x},x !=0`
Write the following in the simplest form:
`sin{2tan^-1sqrt((1-x)/(1+x))}`
Prove the following result-
`tan^-1 63/16 = sin^-1 5/13 + cos^-1 3/5`
Evaluate:
`cos{sin^-1(-7/25)}`
Prove the following result:
`sin^-1 12/13+cos^-1 4/5+tan^-1 63/16=pi`
`sin^-1 63/65=sin^-1 5/13+cos^-1 3/5`
`sin^-1 5/13+cos^-1 3/5=tan^-1 63/16`
Solve the following:
`sin^-1x+sin^-1 2x=pi/3`
Prove that `2tan^-1(sqrt((a-b)/(a+b))tan theta/2)=cos^-1((a costheta+b)/(a+b costheta))`
Write the difference between maximum and minimum values of sin−1 x for x ∈ [− 1, 1].
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 sin−1
\[\left( \sin( -{600}°) \right)\].
Write the value of cos−1 (cos 350°) − sin−1 (sin 350°)
If \[\tan^{- 1} (\sqrt{3}) + \cot^{- 1} x = \frac{\pi}{2},\] find x.
Write the value of \[\tan^{- 1} \left\{ 2\sin\left( 2 \cos^{- 1} \frac{\sqrt{3}}{2} \right) \right\}\]
If \[\cos\left( \tan^{- 1} x + \cot^{- 1} \sqrt{3} \right) = 0\] , find the value of x.
2 tan−1 {cosec (tan−1 x) − tan (cot−1 x)} is equal to
If x < 0, y < 0 such that xy = 1, then tan−1 x + tan−1 y equals
\[\text{ If }\cos^{- 1} \frac{x}{3} + \cos^{- 1} \frac{y}{2} = \frac{\theta}{2}, \text{ then }4 x^2 - 12xy \cos\frac{\theta}{2} + 9 y^2 =\]
If tan−1 3 + tan−1 x = tan−1 8, then x =
sin \[\left\{ 2 \cos^{- 1} \left( \frac{- 3}{5} \right) \right\}\] is equal to
The value of sin \[\left( \frac{1}{4} \sin^{- 1} \frac{\sqrt{63}}{8} \right)\] is
Solve for x : {xcos(cot-1 x) + sin(cot-1 x)}2 = `51/50`
