Advertisements
Advertisements
Question
Write the value of cos−1 \[\left( \tan\frac{3\pi}{4} \right)\]
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 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(tan (3pi)/4)`
Evaluate the following:
`cosec^-1(cosec (13pi)/6)`
Evaluate the following:
`sin(sec^-1 17/8)`
Evaluate the following:
`cosec(cos^-1 3/5)`
Evaluate the following:
`cos(tan^-1 24/7)`
Prove the following result
`sin(cos^-1 3/5+sin^-1 5/13)=63/65`
Evaluate:
`cos{sin^-1(-7/25)}`
Prove the following result:
`tan^-1 1/4+tan^-1 2/9=sin^-1 1/sqrt5`
Solve the following equation for x:
tan−1(x + 2) + tan−1(x − 2) = tan−1 `(8/79)`, x > 0
Solve the following equation for x:
`tan^-1 (x-2)/(x-1)+tan^-1 (x+2)/(x+1)=pi/4`
Evaluate: `cos(sin^-1 3/5+sin^-1 5/13)`
`(9pi)/8-9/4sin^-1 1/3=9/4sin^-1 (2sqrt2)/3`
Solve the equation `cos^-1 a/x-cos^-1 b/x=cos^-1 1/b-cos^-1 1/a`
Prove that: `cos^-1 4/5+cos^-1 12/13=cos^-1 33/65`
`tan^-1 1/7+2tan^-1 1/3=pi/4`
`2sin^-1 3/5-tan^-1 17/31=pi/4`
`2tan^-1 1/5+tan^-1 1/8=tan^-1 4/7`
`2tan^-1 3/4-tan^-1 17/31=pi/4`
Prove that
`sin{tan^-1 (1-x^2)/(2x)+cos^-1 (1-x^2)/(2x)}=1`
If −1 < x < 0, then write the value of `sin^-1((2x)/(1+x^2))+cos^-1((1-x^2)/(1+x^2))`
Write the value of
\[\cos^{- 1} \left( \frac{1}{2} \right) + 2 \sin^{- 1} \left( \frac{1}{2} \right)\].
Write the value of sin \[\left\{ \frac{\pi}{3} - \sin^{- 1} \left( - \frac{1}{2} \right) \right\}\]
Write the value ofWrite the value of \[2 \sin^{- 1} \frac{1}{2} + \cos^{- 1} \left( - \frac{1}{2} \right)\]
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 \[\cos^{- 1} \left( \cos680^\circ \right)\]
The value of \[\cos^{- 1} \left( \cos\frac{5\pi}{3} \right) + \sin^{- 1} \left( \sin\frac{5\pi}{3} \right)\] is
If \[3\sin^{- 1} \left( \frac{2x}{1 + x^2} \right) - 4 \cos^{- 1} \left( \frac{1 - x^2}{1 + x^2} \right) + 2 \tan^{- 1} \left( \frac{2x}{1 - x^2} \right) = \frac{\pi}{3}\] is equal to
It \[\tan^{- 1} \frac{x + 1}{x - 1} + \tan^{- 1} \frac{x - 1}{x} = \tan^{- 1}\] (−7), then the value of x is
If tan−1 (cot θ) = 2 θ, then θ =
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
The domain of \[\cos^{- 1} \left( x^2 - 4 \right)\] is
Prove that : \[\tan^{- 1} \left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) = \frac{\pi}{4} + \frac{1}{2} \cos^{- 1} x^2 ; 1 < x < 1\].
The period of the function f(x) = tan3x is ____________.
The equation sin-1 x – cos-1 x = cos-1 `(sqrt3/2)` has ____________.
