Advertisements
Advertisements
Question
Write the value of cos−1 \[\left( \tan\frac{3\pi}{4} \right)\]
Advertisements
Solution
We have
\[\cos^{- 1} \left( \tan\frac{3\pi}{4} \right) = \cos^{- 1} \left\{ - \tan\left( \pi - \frac{3\pi}{4} \right) \right\} \left[ \because \tan\left( \pi - x \right) = - \tan{x} \right]\]
\[ = \cos^{- 1} \left\{ \tan\left( - \frac{\pi}{4} \right) \right\}\]
\[ = \cos^{- 1} \left\{ - \tan\left( \frac{\pi}{4} \right) \right\}\]
\[ = \cos^{- 1} \left( - 1 \right)\]
\[ = \cos^{- 1} \left( cos\pi \right) \left[ \because cos\pi = - 1 \right]\]
\[ = \pi\]
∴ \[\cos^{- 1} \left( \tan\frac{3\pi}{4} \right) = \pi\]
APPEARS IN
RELATED QUESTIONS
If sin [cot−1 (x+1)] = cos(tan−1x), then find x.
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.
Find the principal values of the following:
`cos^-1(sin (4pi)/3)`
Find the principal values of the following:
`cos^-1(tan (3pi)/4)`
`sin^-1(sin pi/6)`
`sin^-1(sin3)`
`sin^-1(sin4)`
`sin^-1(sin12)`
Evaluate the following:
`cos^-1{cos (5pi)/4}`
Evaluate the following:
`cos^-1{cos ((4pi)/3)}`
Evaluate the following:
`sec^-1(sec pi/3)`
Evaluate the following:
`sec^-1(sec (7pi)/3)`
Evaluate the following:
`sec^-1{sec (-(7pi)/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:
`sin^-1{(sqrt(1+x)+sqrt(1-x))/2},0<x<1`
Evaluate the following:
`cos(tan^-1 24/7)`
Prove the following result
`tan(cos^-1 4/5+tan^-1 2/3)=17/6`
Prove the following result
`sin(cos^-1 3/5+sin^-1 5/13)=63/65`
Evaluate:
`cot{sec^-1(-13/5)}`
`sin^-1x=pi/6+cos^-1x`
Prove the following result:
`tan^-1 1/7+tan^-1 1/13=tan^-1 2/9`
Find the value of `tan^-1 (x/y)-tan^-1((x-y)/(x+y))`
Evaluate: `cos(sin^-1 3/5+sin^-1 5/13)`
Solve the following:
`cos^-1x+sin^-1 x/2=π/6`
If `cos^-1 x/2+cos^-1 y/3=alpha,` then prove that `9x^2-12xy cosa+4y^2=36sin^2a.`
Solve `cos^-1sqrt3x+cos^-1x=pi/2`
Evaluate the following:
`tan 1/2(cos^-1 sqrt5/3)`
Prove that
`sin{tan^-1 (1-x^2)/(2x)+cos^-1 (1-x^2)/(2x)}=1`
Write the value of tan−1x + tan−1 `(1/x)`for x > 0.
Write the value of cos−1 (cos 350°) − sin−1 (sin 350°)
Write the value of tan−1\[\left\{ \tan\left( \frac{15\pi}{4} \right) \right\}\]
If \[\tan^{- 1} (\sqrt{3}) + \cot^{- 1} x = \frac{\pi}{2},\] find x.
Wnte the value of\[\cos\left( \frac{\tan^{- 1} x + \cot^{- 1} x}{3} \right), \text{ when } x = - \frac{1}{\sqrt{3}}\]
If \[\cos^{- 1} \frac{x}{a} + \cos^{- 1} \frac{y}{b} = \alpha, then\frac{x^2}{a^2} - \frac{2xy}{ab}\cos \alpha + \frac{y^2}{b^2} = \]
If \[\cos^{- 1} x > \sin^{- 1} x\], then
Find : \[\int\frac{2 \cos x}{\left( 1 - \sin x \right) \left( 1 + \sin^2 x \right)}dx\] .
If 2 tan−1 (cos θ) = tan−1 (2 cosec θ), (θ ≠ 0), then find the value of θ.
Find the value of x, if tan `[sec^(-1) (1/x) ] = sin ( tan^(-1) 2) , x > 0 `.
tanx is periodic with period ____________.
