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 the following:
3cos−1x = cos−1(4x3 − 3x), `x ∈ [1/2, 1]`
Write the following function in the simplest form:
`tan^(-1) (sqrt((1-cos x)/(1 + cos x)))`, 0 < x < π
Find the value of the following:
`tan^-1 [2 cos (2 sin^-1 1/2)]`
Prove that:
`tan^(-1) sqrtx = 1/2 cos^(-1) (1-x)/(1+x)`, x ∈ [0, 1]
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 the following equation for x: `cos (tan^(-1) x) = sin (cot^(-1) 3/4)`
Solve for x : \[\cos \left( \tan^{- 1} x \right) = \sin \left( \cot^{- 1} \frac{3}{4} \right)\] .
Find the value of the expression in terms of x, with the help of a reference triangle
cos (tan–1 (3x – 1))
Find the value of the expression in terms of x, with the help of a reference triangle
`tan(sin^-1(x + 1/2))`
Find the value of `cot[sin^-1 3/5 + sin^-1 4/5]`
Choose the correct alternative:
If `sin^-1x + sin^-1y = (2pi)/3` ; then `cos^-1x + cos^-1y` is equal to
Choose the correct alternative:
The equation tan–1x – cot–1x = `tan^-1 (1/sqrt(3))` has
Prove that cot–17 + cot–18 + cot–118 = cot–13
Evaluate `cos[cos^-1 ((-sqrt(3))/2) + pi/6]`
The value of the expression `tan (1/2 cos^-1 2/sqrt(5))` is ______.
If y = `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))` for all x, then ______ < y < ______.
The value of cot–1(–x) for all x ∈ R in terms of cot–1x is ______.
`"tan"^-1 1 + "cos"^-1 ((-1)/2) + "sin"^-1 ((-1)/2)`
sin (tan−1 x), where |x| < 1, is equal to:
The value of `"tan"^-1 (1/2) + "tan"^-1(1/3) + "tan"^-1(7/8)` is ____________.
The value of `"tan"^-1 (3/4) + "tan"^-1 (1/7)` is ____________.
`"tan" (pi/4 + 1/2 "cos"^-1 "x") + "tan" (pi/4 - 1/2 "cos"^-1 "x") =` ____________.
`"cos" (2 "tan"^-1 1/7) - "sin" (4 "sin"^-1 1/3) =` ____________.
If `cos^-1(2/(3x)) + cos^-1(3/(4x)) = π/2(x > 3/4)`, then x is equal to ______.
Find the value of `tan^-1 [2 cos (2 sin^-1 1/2)] + tan^-1 1`.
If sin–1x + sin–1y + sin–1z = π, show that `x^2 - y^2 - z^2 + 2yzsqrt(1 - x^2) = 0`
