Advertisements
Advertisements
प्रश्न
Solve the following equation for x: `cos (tan^(-1) x) = sin (cot^(-1) 3/4)`
उत्तर
The given equation is `cos (tan^(-1) x) = sin (cot^(-1) 3/4)`
`cos (tan^(-1) x) = sin(cot^(-1) 3/4)`
`=> cos (tan^(-1) x) = cos(pi/2 - cot^(-1) 3 /4)` `[sintheta = cos(pi/2 - theta)]`
`=> cos(tan^(-1) x) = cos(tan^(-1) (3/4))` `(tan^(-1) x + cot^(-1) x = pi/2)`
`=> tan^(-1) x = tan^(-1) (3/4)`
`=> x = 3/4`
APPEARS IN
संबंधित प्रश्न
Find the value of the given expression.
`tan(sin^(-1) 3/5 + cot^(-1) 3/2)`
`cos^(-1) (cos (7pi)/6)` is equal to ______.
`sin[pi/3 - sin^(-1) (-1/2)]` is equal to ______.
Prove that:
`cos^(-1) 4/5 + cos^(-1) 12/13 = cos^(-1) 33/65`
Prove that:
`cos^(-1) 12/13 + sin^(-1) 3/5 = sin^(-1) 56/65`
sin (tan–1 x), | x| < 1 is equal to ______.
Prove that `3sin^(-1)x = sin^(-1) (3x - 4x^3)`, `x in [-1/2, 1/2]`
Prove that
\[2 \tan^{- 1} \left( \frac{1}{5} \right) + \sec^{- 1} \left( \frac{5\sqrt{2}}{7} \right) + 2 \tan^{- 1} \left( \frac{1}{8} \right) = \frac{\pi}{4}\] .
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)`.
Solve for x : `tan^-1 ((2-"x")/(2+"x")) = (1)/(2)tan^-1 ("x")/(2), "x">0.`
Find the value of `tan(sin^-1 3/5 + cot^-1 3/2)`
Prove that `sin^-1 3/5 - cos^-1 12/13 = sin^-1 16/65`
Prove that cot–17 + cot–18 + cot–118 = cot–13
If `tan^-1x = pi/10` for some x ∈ R, then the value of cot–1x is ______.
Prove that `tan^-1 ((sqrt(1 + x^2) + sqrt(1 - x^2))/((1 + x^2) - sqrt(1 - x^2))) = pi/2 + 1/2 cos^-1x^2`
If a1, a2, a3,...,an is an arithmetic progression with common difference d, then evaluate the following expression.
`tan[tan^-1("d"/(1 + "a"_1 "a"_2)) + tan^-1("d"/(21 + "a"_2 "a"_3)) + tan^-1("d"/(1 + "a"_3 "a"_4)) + ... + tan^-1("d"/(1 + "a"_("n" - 1) "a""n"))]`
The value of cot–1(–x) for all x ∈ R in terms of cot–1x is ______.
If `"cot"^-1 (sqrt"cos" alpha) - "tan"^-1 (sqrt"cos" alpha) = "x",` the sinx is equal to ____________.
`"tan"^-1 1/3 + "tan"^-1 1/5 + "tan"^-1 1/7 = "tan"^-1 1/8 =` ____________.
If tan-1 2x + tan-1 3x = `pi/4,` then x is ____________.
If `"tan"^-1 (("x" - 1)/("x" + 2)) + "tan"^-1 (("x" + 1)/("x" + 2)) = pi/4,` then x is equal to ____________.
The value of `"tan"^-1 (1/2) + "tan"^-1(1/3) + "tan"^-1(7/8)` is ____________.
Solve for x : `"sin"^-1 2"x" + "sin"^-1 3"x" = pi/3`
If `"tan"^-1 2 "x + tan"^-1 3 "x" = pi/4`, then x is ____________.
`"tan" (pi/4 + 1/2 "cos"^-1 "x") + "tan" (pi/4 - 1/2 "cos"^-1 "x") =` ____________.
What is the value of cos (sec–1x + cosec–1x), |x| ≥ 1
`50tan(3tan^-1(1/2) + 2cos^-1(1/sqrt(5))) + 4sqrt(2) tan(1/2tan^-1(2sqrt(2)))` is equal to ______.
The set of all values of k for which (tan–1 x)3 + (cot–1 x)3 = kπ3, x ∈ R, is the internal ______.
Solve:
sin–1(x) + sin–1(1 – x) = cos–1x.
