Advertisements
Advertisements
प्रश्न
Write the value of tan−1\[\left\{ \tan\left( \frac{15\pi}{4} \right) \right\}\]
Advertisements
उत्तर
We have
\[\tan^{- 1} \left\{ \tan\left( \frac{15\pi}{4} \right) \right\} = \tan^{- 1} \left\{ \tan\left( 4\pi - \frac{\pi}{4} \right) \right\}\]
\[ \tan^{- 1} \left\{ - \tan\left( \frac{\pi}{4} \right) \right\} \left[ \because \tan\left( 4\pi - x \right) = - \tan{x} \right]\]
\[ = \tan^{- 1} \left\{ \tan\left( - \frac{\pi}{4} \right) \right\} \]
\[ = - \frac{\pi}{4} \left[ \because \tan^{- 1} \left( \tan{x} \right) = x \right] \]
∴ \[\tan^{- 1} \left\{ \tan\left( \frac{15\pi}{4} \right) \right\} = - \frac{\pi}{4}\]
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`
Find the principal values of the following:
`cos^-1(sin (4pi)/3)`
Evaluate the following:
`cos^-1{cos(-pi/4)}`
Evaluate the following:
`tan^-1(tan (6pi)/7)`
Evaluate the following:
`cosec^-1(cosec (3pi)/4)`
Evaluate the following:
`cot^-1{cot (-(8pi)/3)}`
Write the following in the simplest form:
`tan^-1{x+sqrt(1+x^2)},x in R `
Write the following in the simplest form:
`tan^-1(x/(a+sqrt(a^2-x^2))),-a<x<a`
Write the following in the simplest form:
`sin^-1{(x+sqrt(1-x^2))/sqrt2},-1<x<1`
Evaluate:
`cos(sec^-1x+\text(cosec)^-1x)`,|x|≥1
`tan^-1x+2cot^-1x=(2x)/3`
Prove the following result:
`tan^-1 1/7+tan^-1 1/13=tan^-1 2/9`
Solve the following equation for x:
`tan^-1((1-x)/(1+x))-1/2 tan^-1x` = 0, where x > 0
Evaluate: `cos(sin^-1 3/5+sin^-1 5/13)`
Solve the following:
`cos^-1x+sin^-1 x/2=π/6`
Prove that:
`2sin^-1 3/5=tan^-1 24/7`
`2tan^-1 1/5+tan^-1 1/8=tan^-1 4/7`
Prove that
`sin{tan^-1 (1-x^2)/(2x)+cos^-1 (1-x^2)/(2x)}=1`
Show that `2tan^-1x+sin^-1 (2x)/(1+x^2)` is constant for x ≥ 1, find that constant.
Prove that `2tan^-1(sqrt((a-b)/(a+b))tan theta/2)=cos^-1((a costheta+b)/(a+b costheta))`
Evaluate sin
\[\left( \frac{1}{2} \cos^{- 1} \frac{4}{5} \right)\]
Write the value of cos \[\left( 2 \sin^{- 1} \frac{1}{2} \right)\]
Write the value of cos2 \[\left( \frac{1}{2} \cos^{- 1} \frac{3}{5} \right)\]
Write the value of sin−1 \[\left( \cos\frac{\pi}{9} \right)\]
Write the value ofWrite the value of \[2 \sin^{- 1} \frac{1}{2} + \cos^{- 1} \left( - \frac{1}{2} \right)\]
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 \[\tan^{- 1} \left\{ 2\sin\left( 2 \cos^{- 1} \frac{\sqrt{3}}{2} \right) \right\}\]
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
2 tan−1 {cosec (tan−1 x) − tan (cot−1 x)} is equal to
If α = \[\tan^{- 1} \left( \tan\frac{5\pi}{4} \right) \text{ and }\beta = \tan^{- 1} \left( - \tan\frac{2\pi}{3} \right)\] , then
\[\text{ If } u = \cot^{- 1} \sqrt{\tan \theta} - \tan^{- 1} \sqrt{\tan \theta}\text{ then }, \tan\left( \frac{\pi}{4} - \frac{u}{2} \right) =\]
The value of \[\sin^{- 1} \left( \cos\frac{33\pi}{5} \right)\] is
The value of sin \[\left( \frac{1}{4} \sin^{- 1} \frac{\sqrt{63}}{8} \right)\] is
The value of \[\sin\left( 2\left( \tan^{- 1} 0 . 75 \right) \right)\] is equal to
Find the domain of `sec^(-1) x-tan^(-1)x`
Find the value of x, if tan `[sec^(-1) (1/x) ] = sin ( tan^(-1) 2) , x > 0 `.
The period of the function f(x) = tan3x is ____________.
The value of tan `("cos"^-1 4/5 + "tan"^-1 2/3) =`
