Advertisements
Advertisements
Question
Find the principal values of the following:
`cos^-1(tan (3pi)/4)`
Advertisements
Solution
Let `cos^-1(tan (3pi)/4)=y`
Then,
`cosy=tan (3pi)/4`
We know that the range of the principal value branch is [0,pi]
thus,
`cosy=tan (3pi)/4=-1=cos(pi)`
`=>y=piin[0,pi]`
Hence, the principal value of `cos^-1(tan (3pi)/4)` is π.
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.
`sin^-1(sin (7pi)/6)`
`sin^-1(sin (17pi)/8)`
Evaluate the following:
`cos^-1{cos(-pi/4)}`
Evaluate the following:
`cos^-1{cos ((4pi)/3)}`
Evaluate the following:
`cos^-1(cos4)`
Evaluate the following:
`cos^-1(cos5)`
Evaluate the following:
`cos^-1(cos12)`
Evaluate the following:
`sec^-1(sec (13pi)/4)`
Evaluate the following:
`cosec^-1(cosec (11pi)/6)`
Evaluate the following:
`cot^-1{cot (-(8pi)/3)}`
Write the following in the simplest form:
`cot^-1 a/sqrt(x^2-a^2),| x | > a`
Write the following in the simplest form:
`tan^-1sqrt((a-x)/(a+x)),-a<x<a`
Write the following in the simplest form:
`sin^-1{(x+sqrt(1-x^2))/sqrt2},-1<x<1`
Evaluate:
`cos(tan^-1 3/4)`
`5tan^-1x+3cot^-1x=2x`
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))`
Solve the following equation for x:
tan−1(x + 1) + tan−1(x − 1) = tan−1`8/31`
Evaluate: `cos(sin^-1 3/5+sin^-1 5/13)`
Solve the following:
`sin^-1x+sin^-1 2x=pi/3`
Evaluate the following:
`sin(1/2cos^-1 4/5)`
`tan^-1 1/4+tan^-1 2/9=1/2cos^-1 3/2=1/2sin^-1(4/5)`
`tan^-1 2/3=1/2tan^-1 12/5`
`sin^-1 4/5+2tan^-1 1/3=pi/2`
`2sin^-1 3/5-tan^-1 17/31=pi/4`
`2tan^-1 1/5+tan^-1 1/8=tan^-1 4/7`
`4tan^-1 1/5-tan^-1 1/239=pi/4`
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 of cos\[\left( 2 \sin^{- 1} \frac{1}{3} \right)\]
Write the value of sin−1 (sin 1550°).
Write the value of sin−1 \[\left( \cos\frac{\pi}{9} \right)\]
Write the value of \[\tan^{- 1} \frac{a}{b} - \tan^{- 1} \left( \frac{a - b}{a + b} \right)\]
Evaluate: \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
Write the principal value of \[\cos^{- 1} \left( \cos680^\circ \right)\]
Write the value of \[\tan^{- 1} \left( \frac{1}{x} \right)\] for x < 0 in terms of `cot^-1x`
The value of tan \[\left\{ \cos^{- 1} \frac{1}{5\sqrt{2}} - \sin^{- 1} \frac{4}{\sqrt{17}} \right\}\] is
The value of \[\sin\left( 2\left( \tan^{- 1} 0 . 75 \right) \right)\] is equal to
