Advertisements
Advertisements
प्रश्न
If α = \[\tan^{- 1} \left( \tan\frac{5\pi}{4} \right) \text{ and }\beta = \tan^{- 1} \left( - \tan\frac{2\pi}{3} \right)\] , then
पर्याय
4 α = 3 β
3 α = 4 β
α − β = `(7pi)/12`
none of these
उत्तर
(a) 4 α = 3 β
We know that
\[\tan^{- 1} \left( \tan{x} \right) = x\]
\[\therefore \alpha = \tan^{- 1} \left( \tan\frac{5\pi}{4} \right)\]
\[ = \tan^{- 1} \left\{ \tan\left( \pi + \frac{\pi}{4} \right) \right\}\]
\[ = \tan^{- 1} \left( \tan\frac{\pi}{4} \right)\]
\[ = \frac{\pi}{4}\]
and
\[\beta = \tan^{- 1} \left\{ - \tan\left( \frac{2\pi}{3} \right) \right\}\]
\[ = \tan^{- 1} \left\{ - \tan\left( \pi - \frac{\pi}{3} \right) \right\}\]
\[ = \tan^{- 1} \left\{ \tan\left( \frac{\pi}{3} \right) \right\}\]
\[ = \frac{\pi}{3}\]
\[\therefore 4\alpha = \pi\]
\[3\beta = \pi\]
∴ \[4\alpha = 3\beta\]
APPEARS IN
संबंधित प्रश्न
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 (7pi)/6)`
`sin^-1(sin (5pi)/6)`
`sin^-1(sin (13pi)/7)`
Evaluate the following:
`cos^-1{cos(-pi/4)}`
Evaluate the following:
`cos^-1(cos3)`
Evaluate the following:
`tan^-1(tan pi/3)`
Evaluate the following:
`sec^-1(sec (9pi)/5)`
Write the following in the simplest form:
`sin{2tan^-1sqrt((1-x)/(1+x))}`
Evaluate the following:
`sin(tan^-1 24/7)`
Evaluate the following:
`cosec(cos^-1 3/5)`
Prove the following result
`sin(cos^-1 3/5+sin^-1 5/13)=63/65`
Evaluate:
`cos(tan^-1 3/4)`
Evaluate:
`cos(sec^-1x+\text(cosec)^-1x)`,|x|≥1
If `cos^-1x + cos^-1y =pi/4,` find the value of `sin^-1x+sin^-1y`
`sin(sin^-1 1/5+cos^-1x)=1`
Prove the following result:
`tan^-1 1/7+tan^-1 1/13=tan^-1 2/9`
Solve the following:
`cos^-1x+sin^-1 x/2=π/6`
Prove that: `cos^-1 4/5+cos^-1 12/13=cos^-1 33/65`
`2sin^-1 3/5-tan^-1 17/31=pi/4`
`2tan^-1(1/2)+tan^-1(1/7)=tan^-1(31/17)`
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)`
Find the value of the following:
`tan^-1{2cos(2sin^-1 1/2)}`
Write the value of sin−1
\[\left( \sin( -{600}°) \right)\].
Write the value ofWrite the value of \[2 \sin^{- 1} \frac{1}{2} + \cos^{- 1} \left( - \frac{1}{2} \right)\]
Evaluate: \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
2 tan−1 {cosec (tan−1 x) − tan (cot−1 x)} is equal to
Let f (x) = `e^(cos^-1){sin(x+pi/3}.`
Then, f (8π/9) =
\[\tan^{- 1} \frac{1}{11} + \tan^{- 1} \frac{2}{11}\] is equal to
The value of sin \[\left( \frac{1}{4} \sin^{- 1} \frac{\sqrt{63}}{8} \right)\] is
If \[\sin^{- 1} \left( \frac{2a}{1 - a^2} \right) + \cos^{- 1} \left( \frac{1 - a^2}{1 + a^2} \right) = \tan^{- 1} \left( \frac{2x}{1 - x^2} \right),\text{ where }a, x \in \left( 0, 1 \right)\] , then, the value of x is
If x > 1, then \[2 \tan^{- 1} x + \sin^{- 1} \left( \frac{2x}{1 + x^2} \right)\] is equal to
If 2 tan−1 (cos θ) = tan−1 (2 cosec θ), (θ ≠ 0), then find the value of θ.
The value of sin `["cos"^-1 (7/25)]` is ____________.
The equation sin-1 x – cos-1 x = cos-1 `(sqrt3/2)` has ____________.
