Advertisements
Advertisements
प्रश्न
`2tan^-1 3/4-tan^-1 17/31=pi/4`
Advertisements
उत्तर
LHS = `2tan^-1 3/4-tan^-1 17/31`
`=tan^-1{(2xx3/4)/(1-(3/4)^2)}-tan^-1 17/31` `[because2tan^-1x=tan^-1{(2x)/(1-x^2)}]`
`=tan^-1{(3/2)/(7/16)}-tan^-1 17/31`
`=tan^-1 24/7-tan^-1 17/31`
`=tan^-1((24/7-17/31)/(1+24/7xx17/31))` `[becausetan^-1x-tan^-1y=tan^-1((x-y)/(1+xy))]`
`=tan^-1((625/217)/(625/217))`
`=tan^-1 1=pi/4=` RHS
APPEARS IN
संबंधित प्रश्न
Find the value of the following: `tan(1/2)[sin^(-1)((2x)/(1+x^2))+cos^(-1)((1-y^2)/(1+y^2))],|x| <1,y>0 and xy <1`
Solve the equation for x:sin−1x+sin−1(1−x)=cos−1x
Find the domain of `f(x) =2cos^-1 2x+sin^-1x.`
`sin^-1(sin3)`
`sin^-1(sin12)`
`sin^-1(sin2)`
Evaluate the following:
`cos^-1{cos(-pi/4)}`
Evaluate the following:
`sec^-1(sec (13pi)/4)`
Evaluate the following:
`cot^-1(cot pi/3)`
Write the following in the simplest form:
`tan^-1{sqrt(1+x^2)-x},x in R`
Write the following in the simplest form:
`sin{2tan^-1sqrt((1-x)/(1+x))}`
Evaluate the following:
`cos(tan^-1 24/7)`
Evaluate:
`cos(tan^-1 3/4)`
Evaluate:
`cos(sec^-1x+\text(cosec)^-1x)`,|x|≥1
Prove the following result:
`sin^-1 12/13+cos^-1 4/5+tan^-1 63/16=pi`
Solve the following equation for x:
cot−1x − cot−1(x + 2) =`pi/12`, x > 0
Evaluate: `cos(sin^-1 3/5+sin^-1 5/13)`
`sin^-1 63/65=sin^-1 5/13+cos^-1 3/5`
If `cos^-1 x/2+cos^-1 y/3=alpha,` then prove that `9x^2-12xy cosa+4y^2=36sin^2a.`
Evaluate the following:
`tan 1/2(cos^-1 sqrt5/3)`
Evaluate the following:
`sin(1/2cos^-1 4/5)`
`tan^-1 1/7+2tan^-1 1/3=pi/4`
`4tan^-1 1/5-tan^-1 1/239=pi/4`
Solve the following equation for x:
`tan^-1((2x)/(1-x^2))+cot^-1((1-x^2)/(2x))=(2pi)/3,x>0`
Solve the following equation for x:
`cos^-1((x^2-1)/(x^2+1))+1/2tan^-1((2x)/(1-x^2))=(2x)/3`
Write the value of tan−1 x + tan−1 `(1/x)` for x < 0.
What is the value of cos−1 `(cos (2x)/3)+sin^-1(sin (2x)/3)?`
Evaluate: \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
Write the value of \[\tan^{- 1} \left\{ 2\sin\left( 2 \cos^{- 1} \frac{\sqrt{3}}{2} \right) \right\}\]
Write the value of \[\cos^{- 1} \left( \cos\frac{14\pi}{3} \right)\]
The set of values of `\text(cosec)^-1(sqrt3/2)`
Write the value of `cot^-1(-x)` for all `x in R` in terms of `cot^-1(x)`
Find the value of \[\tan^{- 1} \left( \tan\frac{9\pi}{8} \right)\]
If \[\tan^{- 1} \left( \frac{\sqrt{1 + x^2} - \sqrt{1 - x^2}}{\sqrt{1 + x^2} + \sqrt{1 - x^2}} \right)\] = α, then x2 =
\[\tan^{- 1} \frac{1}{11} + \tan^{- 1} \frac{2}{11}\] is equal to
sin \[\left\{ 2 \cos^{- 1} \left( \frac{- 3}{5} \right) \right\}\] is equal to
If 2 tan−1 (cos θ) = tan−1 (2 cosec θ), (θ ≠ 0), then find the value of θ.
Write the value of \[\cos^{- 1} \left( - \frac{1}{2} \right) + 2 \sin^{- 1} \left( \frac{1}{2} \right)\] .
Find the domain of `sec^(-1)(3x-1)`.
Find the value of `sin^-1(cos((33π)/5))`.
