Advertisements
Advertisements
प्रश्न
Prove that: `tan^(-1)(1/2)+tan^(-1)(1/5)+tan^(-1)(1/8)=pi/4`
Advertisements
उत्तर
To prove `tan^(-1)(1/2)+tan^(-1)(1/5)+tan^(-1)(1/8)=pi/4` we will use the following formula
`tan^(-1)+tan^(-1)y=tan^(-1)((x+y)/(1-xy)),xy<1`
`Let S=tan^(-1)(1/2)+tan^(-1)(1/5)+tan^(-1)(1/8)`
`S=[tan^(-1)(1/2)+tan^(-1)(1/5)]+tan^(-1)(1/8)`
`S=tan^(-1)((1/2+1/5)/(1-1/2 xx 1/5))+tan^(-1)(1/8)`
`S=tan^(-1)(7/9)+tan^(-1)(1/8)`
`=tan^(-1)((7/9+1/8)/(1-(7/9)xx(1/8)))`
`=tan^(-1)((56+9)/(72-7))`
`S=tan^(-1)(65/65)=tan^(-1)1=pi/4`
Hence, `tan^(-1)(1/2)+tan^(-1)(1/5)+tan^(-1)(1/8)=pi/4`
APPEARS IN
संबंधित प्रश्न
Prove `tan^(-1) 2/11 + tan^(-1) 7/24 = tan^(-1) 1/2`
Find the value of the given expression.
`tan(sin^(-1) 3/5 + cot^(-1) 3/2)`
sin–1 (1 – x) – 2 sin–1 x = `pi/2`, then x is equal to ______.
Solve `tan^(-1) - tan^(-1) (x - y)/(x+y)` is equal to
(A) `pi/2`
(B). `pi/3`
(C) `pi/4`
(D) `(-3pi)/4`
Solve for x : \[\cos \left( \tan^{- 1} x \right) = \sin \left( \cot^{- 1} \frac{3}{4} \right)\] .
If y = `(x sin^-1 x)/sqrt(1 -x^2)`, prove that: `(1 - x^2)dy/dx = x + y/x`
If tan-1 x - cot-1 x = tan-1 `(1/sqrt(3)),`x> 0 then find the value of x and hence find the value of sec-1 `(2/x)`.
Find the value, if it exists. If not, give the reason for non-existence
`sin^-1 [sin 5]`
Find the value of the expression in terms of x, with the help of a reference triangle
sin (cos–1(1 – x))
Find the value of `sin^-1[cos(sin^-1 (sqrt(3)/2))]`
Find the value of `cot[sin^-1 3/5 + sin^-1 4/5]`
Prove that `tan^-1x + tan^-1 (2x)/(1 - x^2) = tan^-1 (3x - x^3)/(1 - 3x^2), |x| < 1/sqrt(3)`
Evaluate: `sin^-1 [cos(sin^-1 sqrt(3)/2)]`
Evaluate `cos[sin^-1 1/4 + sec^-1 4/3]`
Prove that `sin^-1 8/17 + sin^-1 3/5 = sin^-1 7/85`
If `"sec" theta = "x" + 1/(4 "x"), "x" in "R, x" ne 0,`then the value of `"sec" theta + "tan" theta` is ____________.
The value of `"tan"^-1 (1/2) + "tan"^-1 (1/3) + "tan"^-1 (7/8)` is ____________.
If `"tan"^-1 ("cot" theta) = 2theta, "then" theta` is equal to ____________.
The domain of the function defind by f(x) `= "sin"^-1 sqrt("x" - 1)` is ____________.
`"cos" (2 "tan"^-1 1/7) - "sin" (4 "sin"^-1 1/3) =` ____________.
If x = a sec θ, y = b tan θ, then `("d"^2"y")/("dx"^2)` at θ = `π/6` is:
Simplest form of `tan^-1 ((sqrt(1 + cos "x") + sqrt(1 - cos "x"))/(sqrt(1 + cos "x") - sqrt(1 - cos "x")))`, `π < "x" < (3π)/2` is:
`"cos"^-1 (1/2)`
`"sin"^-1 ((-1)/2)`
What is the value of cos (sec–1x + cosec–1x), |x| ≥ 1
Find the value of `sin^-1 [sin((13π)/7)]`
If `cos^-1(2/(3x)) + cos^-1(3/(4x)) = π/2(x > 3/4)`, then x is equal to ______.
