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
Find the value of the following: `tan(1/2)[sin^(-1)((2x)/(1+x^2))+cos^(-1)((1-y^2)/(1+y^2))],|x| <1,y>0 and xy <1`
Solve the following for x :
`tan^(-1)((x-2)/(x-3))+tan^(-1)((x+2)/(x+3))=pi/4,|x|<1`
If tan-1x+tan-1y=π/4,xy<1, then write the value of x+y+xy.
Find the principal values of the following:
`cos^-1(-sqrt3/2)`
`sin^-1(sin (5pi)/6)`
`sin^-1(sin4)`
Evaluate the following:
`tan^-1(tan pi/3)`
Evaluate the following:
`cot^-1(cot (9pi)/4)`
Evaluate the following:
`cos(tan^-1 24/7)`
Evaluate:
`sec{cot^-1(-5/12)}`
If `sin^-1x+sin^-1y=pi/3` and `cos^-1x-cos^-1y=pi/6`, find the values of x and y.
Solve the following equation for x:
tan−1(x + 1) + tan−1(x − 1) = tan−1`8/31`
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
Solve the following equation for x:
`tan^-1 (x-2)/(x-1)+tan^-1 (x+2)/(x+1)=pi/4`
Solve the following:
`cos^-1x+sin^-1 x/2=π/6`
Solve the equation `cos^-1 a/x-cos^-1 b/x=cos^-1 1/b-cos^-1 1/a`
Evaluate the following:
`tan{2tan^-1 1/5-pi/4}`
Evaluate the following:
`sin(2tan^-1 2/3)+cos(tan^-1sqrt3)`
`2tan^-1(1/2)+tan^-1(1/7)=tan^-1(31/17)`
`4tan^-1 1/5-tan^-1 1/239=pi/4`
If `sin^-1 (2a)/(1+a^2)+sin^-1 (2b)/(1+b^2)=2tan^-1x,` Prove that `x=(a+b)/(1-ab).`
Solve the following equation for x:
`tan^-1 1/4+2tan^-1 1/5+tan^-1 1/6+tan^-1 1/x=pi/4`
Solve the following equation for x:
`tan^-1((x-2)/(x-1))+tan^-1((x+2)/(x+1))=pi/4`
Write the value of `sin^-1((-sqrt3)/2)+cos^-1((-1)/2)`
If x < 0, then write the value of cos−1 `((1-x^2)/(1+x^2))` in terms of tan−1 x.
Write the value of cos\[\left( 2 \sin^{- 1} \frac{1}{3} \right)\]
Write the value of cos−1 (cos 350°) − sin−1 (sin 350°)
Write the value of \[\tan^{- 1} \frac{a}{b} - \tan^{- 1} \left( \frac{a - b}{a + b} \right)\]
If 4 sin−1 x + cos−1 x = π, then what is the value of x?
Write the principal value of `sin^-1(-1/2)`
Write the principal value of \[\cos^{- 1} \left( \cos\frac{2\pi}{3} \right) + \sin^{- 1} \left( \sin\frac{2\pi}{3} \right)\]
Write the principal value of \[\cos^{- 1} \left( \cos680^\circ \right)\]
The value of tan \[\left\{ \cos^{- 1} \frac{1}{5\sqrt{2}} - \sin^{- 1} \frac{4}{\sqrt{17}} \right\}\] is
If 4 cos−1 x + sin−1 x = π, then the value of x is
It \[\tan^{- 1} \frac{x + 1}{x - 1} + \tan^{- 1} \frac{x - 1}{x} = \tan^{- 1}\] (−7), then the value of x is
Find the value of `sin^-1(cos((33π)/5))`.
