Advertisements
Advertisements
Question
Evaluate:
`cos{sin^-1(-7/25)}`
Solution
`cos{sin^-1(-7/25)}=cos{-sin^-1(7/25)}`
`=cos{sin^-1(7/25)}`
`=cos{cos^-1sqrt(1-(7/25)^2)}`
`=cos{cos^-1 24/25}`
`=24/25`
APPEARS IN
RELATED QUESTIONS
If sin [cot−1 (x+1)] = cos(tan−1x), then find x.
If tan-1x+tan-1y=π/4,xy<1, then write the value of x+y+xy.
Prove that
`tan^(-1) [(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))]=pi/4-1/2 cos^(-1)x,-1/sqrt2<=x<=1`
Find the principal values of the following:
`cos^-1(-sqrt3/2)`
`sin^-1(sin pi/6)`
`sin^-1(sin (5pi)/6)`
Evaluate the following:
`cos^-1{cos (5pi)/4}`
Evaluate the following:
`sec^-1(sec (7pi)/3)`
Evaluate the following:
`sec^-1{sec (-(7pi)/3)}`
Evaluate the following:
`cosec^-1(cosec (3pi)/4)`
Evaluate the following:
`cosec^-1{cosec (-(9pi)/4)}`
Evaluate the following:
`cot^-1(cot (4pi)/3)`
Evaluate:
`sec{cot^-1(-5/12)}`
Evaluate:
`cosec{cot^-1(-12/5)}`
Evaluate:
`sin(tan^-1x+tan^-1 1/x)` for x < 0
Evaluate: `cos(sin^-1 3/5+sin^-1 5/13)`
`sin^-1 5/13+cos^-1 3/5=tan^-1 63/16`
`sin^-1 4/5+2tan^-1 1/3=pi/2`
`2tan^-1(1/2)+tan^-1(1/7)=tan^-1(31/17)`
Prove that
`tan^-1((1-x^2)/(2x))+cot^-1((1-x^2)/(2x))=pi/2`
What is the value of cos−1 `(cos (2x)/3)+sin^-1(sin (2x)/3)?`
Evaluate sin
\[\left( \frac{1}{2} \cos^{- 1} \frac{4}{5} \right)\]
Write the value of cos2 \[\left( \frac{1}{2} \cos^{- 1} \frac{3}{5} \right)\]
If x < 0, y < 0 such that xy = 1, then write the value of tan−1 x + tan−1 y.
Write the principal value of \[\tan^{- 1} 1 + \cos^{- 1} \left( - \frac{1}{2} \right)\]
Write the principal value of `tan^-1sqrt3+cot^-1sqrt3`
Write the principal value of \[\cos^{- 1} \left( \cos680^\circ \right)\]
If \[\cos\left( \sin^{- 1} \frac{2}{5} + \cos^{- 1} x \right) = 0\], find the value of x.
2 tan−1 {cosec (tan−1 x) − tan (cot−1 x)} is equal to
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 x < 0, y < 0 such that xy = 1, then tan−1 x + tan−1 y equals
Let f (x) = `e^(cos^-1){sin(x+pi/3}.`
Then, f (8π/9) =
If 4 cos−1 x + sin−1 x = π, then the value of x is
The value of sin \[\left( \frac{1}{4} \sin^{- 1} \frac{\sqrt{63}}{8} \right)\] is
Find the domain of `sec^(-1)(3x-1)`.
The value of sin `["cos"^-1 (7/25)]` is ____________.
