Advertisements
Advertisements
प्रश्न
Prove the following result
`tan(cos^-1 4/5+tan^-1 2/3)=17/6`
Advertisements
उत्तर
LHS=`tan(cos^-1 4/5+tan^-1 2/3)=tan(tan^-1 sqrt(1-(4/5)^2)/(4/5)+tan^-1 2/3)` `[thereforecos^-1x=tan^-1(sqrt(1-x^2)/x)]`
`=tan(tan^-1 3/4+tan^-1 2/3)`
`=tan[tan^-1((3/4+2/3)/(1-3/4xx2/3))]` `[thereforetan^-1x+tan^-1y=tan^-1((x+y)/(1-xy))]`
`=tan[tan^-1((17/12)/(6/12))`
`=tan[tan^-1 17/6]`
`=17/6=`RHS
APPEARS IN
संबंधित प्रश्न
Write the value of `tan(2tan^(-1)(1/5))`
Solve the following for x :
`tan^(-1)((x-2)/(x-3))+tan^(-1)((x+2)/(x+3))=pi/4,|x|<1`
If sin [cot−1 (x+1)] = cos(tan−1x), then find x.
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(-sqrt3/2)`
Find the principal values of the following:
`cos^-1(sin (4pi)/3)`
`sin^-1(sin (13pi)/7)`
`sin^-1(sin (17pi)/8)`
`sin^-1(sin4)`
Evaluate the following:
`cos^-1{cos (5pi)/4}`
Evaluate the following:
`cos^-1(cos4)`
Evaluate the following:
`tan^-1(tan12)`
Evaluate the following:
`cot^-1(cot pi/3)`
Evaluate the following:
`cot^-1(cot (9pi)/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^-1sqrt((a-x)/(a+x)),-a<x<a`
Evaluate:
`cot{sec^-1(-13/5)}`
Evaluate:
`tan{cos^-1(-7/25)}`
Evaluate: `sin{cos^-1(-3/5)+cot^-1(-5/12)}`
Prove the following result:
`tan^-1 1/7+tan^-1 1/13=tan^-1 2/9`
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-2)/(x-1)+tan^-1 (x+2)/(x+1)=pi/4`
Solve `cos^-1sqrt3x+cos^-1x=pi/2`
`tan^-1 1/4+tan^-1 2/9=1/2cos^-1 3/2=1/2sin^-1(4/5)`
`2tan^-1 1/5+tan^-1 1/8=tan^-1 4/7`
Show that `2tan^-1x+sin^-1 (2x)/(1+x^2)` is constant for x ≥ 1, find that constant.
Write the value of sin (cot−1 x).
Write the value of cos−1 \[\left( \tan\frac{3\pi}{4} \right)\]
Write the value of cos \[\left( 2 \sin^{- 1} \frac{1}{2} \right)\]
Write the value ofWrite the value of \[2 \sin^{- 1} \frac{1}{2} + \cos^{- 1} \left( - \frac{1}{2} \right)\]
Write the value of \[\sin^{- 1} \left( \frac{1}{3} \right) - \cos^{- 1} \left( - \frac{1}{3} \right)\]
Write the principal value of \[\tan^{- 1} 1 + \cos^{- 1} \left( - \frac{1}{2} \right)\]
If \[\cos\left( \sin^{- 1} \frac{2}{5} + \cos^{- 1} x \right) = 0\], find the value of x.
The value of \[\sin^{- 1} \left( \cos\frac{33\pi}{5} \right)\] is
In a ∆ ABC, if C is a right angle, then
\[\tan^{- 1} \left( \frac{a}{b + c} \right) + \tan^{- 1} \left( \frac{b}{c + a} \right) =\]
\[\cot\left( \frac{\pi}{4} - 2 \cot^{- 1} 3 \right) =\]
The equation sin-1 x – cos-1 x = cos-1 `(sqrt3/2)` has ____________.
Find the value of `sin^-1(cos((33π)/5))`.
