Advertisements
Advertisements
प्रश्न
Prove the following result
`sin(cos^-1 3/5+sin^-1 5/13)=63/65`
Advertisements
उत्तर
LHS `=sin(cos^-1 3/5+sin^-1 5/13)`
`=sin[sin^-1sqrt(1-(3/5)^2)+sin^-1 5/13]`
`=sin[sin^-1 4/5+sin^-1 5/13]`
`=sin{sin^-1[4/5xxsqrt(1-(5/13)^2)+5/13xxsqrt(1-(4/5)^2)]}`
`=sin[sin^-1(48/65+15/65)]`
`=sin(sin^-1 63/65)`
`=63/65 =`RHS
APPEARS IN
संबंधित प्रश्न
Solve the following for x:
`sin^(-1)(1-x)-2sin^-1 x=pi/2`
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.
If `(sin^-1x)^2 + (sin^-1y)^2+(sin^-1z)^2=3/4pi^2,` find the value of x2 + y2 + z2
Evaluate the following:
`cos^-1{cos ((4pi)/3)}`
Evaluate the following:
`tan^-1(tan1)`
Evaluate the following:
`sec^-1(sec (5pi)/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:
`tan^-1sqrt((a-x)/(a+x)),-a<x<a`
Evaluate the following:
`sin(cos^-1 5/13)`
Evaluate the following:
`cosec(cos^-1 3/5)`
Prove the following result
`cos(sin^-1 3/5+cot^-1 3/2)=6/(5sqrt13)`
Solve: `cos(sin^-1x)=1/6`
Evaluate:
`sin(tan^-1x+tan^-1 1/x)` for x > 0
If `(sin^-1x)^2+(cos^-1x)^2=(17pi^2)/36,` Find x
`sin(sin^-1 1/5+cos^-1x)=1`
Prove the following result:
`sin^-1 12/13+cos^-1 4/5+tan^-1 63/16=pi`
Solve the following equation for x:
cot−1x − cot−1(x + 2) =`pi/12`, x > 0
`sin^-1 5/13+cos^-1 3/5=tan^-1 63/16`
Solve the following equation for x:
`tan^-1((2x)/(1-x^2))+cot^-1((1-x^2)/(2x))=(2pi)/3,x>0`
Solve the following equation for x:
`cos^-1((x^2-1)/(x^2+1))+1/2tan^-1((2x)/(1-x^2))=(2x)/3`
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 \[\tan^{- 1} (\sqrt{3}) + \cot^{- 1} x = \frac{\pi}{2},\] find x.
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 value of \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
If sin−1 x − cos−1 x = `pi/6` , then x =
sin\[\left[ \cot^{- 1} \left\{ \tan\left( \cos^{- 1} x \right) \right\} \right]\] is equal to
If x < 0, y < 0 such that xy = 1, then tan−1 x + tan−1 y equals
If \[\cos^{- 1} \frac{x}{2} + \cos^{- 1} \frac{y}{3} = \theta,\] then 9x2 − 12xy cos θ + 4y2 is equal to
If x > 1, then \[2 \tan^{- 1} x + \sin^{- 1} \left( \frac{2x}{1 + x^2} \right)\] is equal to
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 : \[\tan^{- 1} \left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) = \frac{\pi}{4} + \frac{1}{2} \cos^{- 1} x^2 ; 1 < x < 1\].
If 2 tan−1 (cos θ) = tan−1 (2 cosec θ), (θ ≠ 0), then find the value of θ.
Write the value of \[\cos^{- 1} \left( - \frac{1}{2} \right) + 2 \sin^{- 1} \left( \frac{1}{2} \right)\] .
Find the value of `sin^-1(cos((33π)/5))`.
