Advertisements
Advertisements
Question
Prove that:
`2sin^-1 3/5=tan^-1 24/7`
Advertisements
Solution
`2sin^-1 3/5`
= `2tan^-1 3/sqrt(5^2 - 3^2) ...[sin^-1 p/h = tan^-1 p/sqrt(h^2 - p^2)]`
= `2 tan^-1 3/sqrt(25 - 9)`
= `2 tan^-1 3/sqrt16`
= `2tan^-1 3/4`
= `tan^-1 (2 xx 3/4)/(1 - (3/4)^2) ...[2tan^-1 x = tan^-1 (2x)/(1 - x^2)]`
= `tan^-1 (3/2)/(1 - 9/16)`
= `tan^-1 (3/2)/((16 - 9)/16)`
= `tan^-1 (3/2)/(7/16)`
= `tan^-1 (3/2 xx 16/7)`
= `tan^-1 (3/1 xx 8/7)`
= `tan^-1 24/7`
APPEARS IN
RELATED QUESTIONS
Find the domain of `f(x) =2cos^-1 2x+sin^-1x.`
Evaluate the following:
`cos^-1{cos (13pi)/6}`
Evaluate the following:
`cos^-1(cos5)`
Evaluate the following:
`sec^-1(sec pi/3)`
Evaluate the following:
`cot^-1(cot (4pi)/3)`
Write the following in the simplest form:
`tan^-1{sqrt(1+x^2)-x},x in R`
Evaluate the following:
`sec(sin^-1 12/13)`
Prove the following result
`cos(sin^-1 3/5+cot^-1 3/2)=6/(5sqrt13)`
Prove the following result-
`tan^-1 63/16 = sin^-1 5/13 + cos^-1 3/5`
Solve the following equation for x:
tan−1(x + 2) + tan−1(x − 2) = tan−1 `(8/79)`, x > 0
`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`
`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`
Find the value of the following:
`tan^-1{2cos(2sin^-1 1/2)}`
Solve the following equation for x:
`3sin^-1 (2x)/(1+x^2)-4cos^-1 (1-x^2)/(1+x^2)+2tan^-1 (2x)/(1-x^2)=pi/3`
Write the value of `sin^-1((-sqrt3)/2)+cos^-1((-1)/2)`
Write the value of tan−1x + tan−1 `(1/x)`for x > 0.
Write the value of cos \[\left( 2 \sin^{- 1} \frac{1}{2} \right)\]
If tan−1 x + tan−1 y = `pi/4`, then write the value of x + y + xy.
If x < 0, y < 0 such that xy = 1, then write the value of tan−1 x + tan−1 y.
Write the value of \[\tan^{- 1} \left\{ 2\sin\left( 2 \cos^{- 1} \frac{\sqrt{3}}{2} \right) \right\}\]
Find the value of \[\cos^{- 1} \left( \cos\frac{13\pi}{6} \right)\]
Find the value of \[\tan^{- 1} \left( \tan\frac{9\pi}{8} \right)\]
sin\[\left[ \cot^{- 1} \left\{ \tan\left( \cos^{- 1} x \right) \right\} \right]\] is equal to
If α = \[\tan^{- 1} \left( \tan\frac{5\pi}{4} \right) \text{ and }\beta = \tan^{- 1} \left( - \tan\frac{2\pi}{3} \right)\] , then
\[\tan^{- 1} \frac{1}{11} + \tan^{- 1} \frac{2}{11}\] is equal to
The value of \[\sin^{- 1} \left( \cos\frac{33\pi}{5} \right)\] is
sin \[\left\{ 2 \cos^{- 1} \left( \frac{- 3}{5} \right) \right\}\] is equal to
Find : \[\int\frac{2 \cos x}{\left( 1 - \sin x \right) \left( 1 + \sin^2 x \right)}dx\] .
Find the domain of `sec^(-1)(3x-1)`.
Find the real solutions of the equation
`tan^-1 sqrt(x(x + 1)) + sin^-1 sqrt(x^2 + x + 1) = pi/2`
The value of sin `["cos"^-1 (7/25)]` is ____________.
