Advertisements
Advertisements
Question
sin \[\left\{ 2 \cos^{- 1} \left( \frac{- 3}{5} \right) \right\}\] is equal to
Options
`6/25`
`24/25`
`4/5`
`-24/25`
Advertisements
Solution
(d) `-24/25`
Let \[\cos^{- 1} \left( - \frac{3}{5} \right) = x, 0 \leq x \leq \pi\]
Then,
`cosx=-3/5`
\[\therefore \sin{x} = \sqrt{1 - \cos^2 x} = \sqrt{1 - \left( - \frac{3}{5} \right)^2} = \sqrt{\frac{16}{25}} = \frac{4}{5}\]
Now,
\[\sin\left\{ 2 \cos^{- 1} \left( - \frac{3}{5} \right) \right\} = \sin\left( 2x \right)\]
\[ = 2\sin{x} \cos{x}\]
\[ = 2 \times \frac{4}{5} \times \frac{- 3}{5}\]
\[ = - \frac{24}{25}\]
APPEARS IN
RELATED QUESTIONS
If `tan^(-1)((x-2)/(x-4)) +tan^(-1)((x+2)/(x+4))=pi/4` ,find the value of x
Find the principal values of the following:
`cos^-1(sin (4pi)/3)`
Find the principal values of the following:
`cos^-1(tan (3pi)/4)`
Evaluate the following:
`cos^-1{cos ((4pi)/3)}`
Evaluate the following:
`cos^-1(cos3)`
Evaluate the following:
`tan^-1(tan (6pi)/7)`
Evaluate the following:
`tan^-1(tan2)`
Evaluate the following:
`sec^-1(sec pi/3)`
Evaluate the following:
`cosec^-1(cosec (11pi)/6)`
Evaluate the following:
`cot^-1(cot (9pi)/4)`
Evaluate the following:
`cot^-1{cot ((21pi)/4)}`
Write the following in the simplest form:
`tan^-1{sqrt(1+x^2)-x},x in R`
Write the following in the simplest form:
`tan^-1{(sqrt(1+x^2)-1)/x},x !=0`
Prove the following result
`tan(cos^-1 4/5+tan^-1 2/3)=17/6`
Evaluate:
`cot(sin^-1 3/4+sec^-1 4/3)`
Evaluate:
`sin(tan^-1x+tan^-1 1/x)` for x > 0
If `cos^-1x + cos^-1y =pi/4,` find the value of `sin^-1x+sin^-1y`
`tan^-1x+2cot^-1x=(2x)/3`
Solve the following equation for x:
tan−1(x + 1) + tan−1(x − 1) = tan−1`8/31`
Solve the following equation for x:
tan−1(x −1) + tan−1x tan−1(x + 1) = tan−13x
Solve the following equation for x:
`tan^-1 (x-2)/(x-1)+tan^-1 (x+2)/(x+1)=pi/4`
Find the value of the following:
`cos(sec^-1x+\text(cosec)^-1x),` | x | ≥ 1
Prove that:
`tan^-1 (2ab)/(a^2-b^2)+tan^-1 (2xy)/(x^2-y^2)=tan^-1 (2alphabeta)/(alpha^2-beta^2),` where `alpha=ax-by and beta=ay+bx.`
Write the value of tan−1x + tan−1 `(1/x)`for x > 0.
Write the value ofWrite the value of \[2 \sin^{- 1} \frac{1}{2} + \cos^{- 1} \left( - \frac{1}{2} \right)\]
If \[\tan^{- 1} (\sqrt{3}) + \cot^{- 1} x = \frac{\pi}{2},\] find x.
If x < 0, y < 0 such that xy = 1, then write the value of tan−1 x + tan−1 y.
What is the principal value of `sin^-1(-sqrt3/2)?`
Write the value of \[\tan\left( 2 \tan^{- 1} \frac{1}{5} \right)\]
Write the value of \[\sec^{- 1} \left( \frac{1}{2} \right)\]
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 x < 0, y < 0 such that xy = 1, then tan−1 x + tan−1 y equals
The value of sin \[\left( \frac{1}{4} \sin^{- 1} \frac{\sqrt{63}}{8} \right)\] is
Find the simplified form of `cos^-1 (3/5 cosx + 4/5 sin x)`, where x ∈ `[(-3pi)/4, pi/4]`
The value of tan `("cos"^-1 4/5 + "tan"^-1 2/3) =`
The equation sin-1 x – cos-1 x = cos-1 `(sqrt3/2)` has ____________.
