Advertisements
Advertisements
प्रश्न
Write the following function in the simplest form:
`tan^-1 ((cos x - sin x)/(cos x + sin x)), (-pi)/4 < x < (3 pi)/4`
उत्तर
`"tan"^-1 (("cos x - sin x")/("cos x + sin x"))`
`Rightarrow "tan"^-1 ((1 - "sin x"/"cos x")/(1 + "sin x"/"cos x"))`
`Rightarrow "tan"^-1 ((1 - "tan x")/(1 + "tan x"))`
`Rightarrow "tan"^-1 (1) - "tan"^-1 ("tan x")`
`Rightarrow pi/4 - "x"`
संबंधित प्रश्न
Prove that `2tan^(-1)(1/5)+sec^(-1)((5sqrt2)/7)+2tan^(-1)(1/8)=pi/4`
Write the following function in the simplest form:
`tan^(-1) (sqrt(1+x^2) -1)/x, x != 0`
Write the following function in the simplest form:
`tan^(-1) ((3a^2 x - x^3)/(a^3 - 3ax^2)), a > 0; (-a)/sqrt3 <= x a/sqrt3`
Find the value of the following:
`tan^-1 [2 cos (2 sin^-1 1/2)]`
Prove that:
`cos^(-1) 4/5 + cos^(-1) 12/13 = cos^(-1) 33/65`
sin–1 (1 – x) – 2 sin–1 x = `pi/2` , then x is equal to ______.
Prove that `tan {pi/4 + 1/2 cos^(-1) a/b} + tan {pi/4 - 1/2 cos^(-1) a/b} = (2b)/a`
Prove that
\[2 \tan^{- 1} \left( \frac{1}{5} \right) + \sec^{- 1} \left( \frac{5\sqrt{2}}{7} \right) + 2 \tan^{- 1} \left( \frac{1}{8} \right) = \frac{\pi}{4}\] .
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
`tan(sin^-1(x + 1/2))`
Find the value of `cot[sin^-1 3/5 + sin^-1 4/5]`
Find the number of solutions of the equation `tan^-1 (x - 1) + tan^-1x + tan^-1(x + 1) = tan^-1(3x)`
Choose the correct alternative:
`sin^-1 (tan pi/4) - sin^-1 (sqrt(3/x)) = pi/6`. Then x is a root of the equation
Choose the correct alternative:
If `sin^-1x + cot^-1 (1/2) = pi/2`, then x is equal to
Evaluate tan (tan–1(– 4)).
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`
Prove that `sin^-1 8/17 + sin^-1 3/5 = sin^-1 7/85`
Show that `tan(1/2 sin^-1 3/4) = (4 - sqrt(7))/3` and justify why the other value `(4 + sqrt(7))/3` is ignored?
If cos–1x > sin–1x, then ______.
The value of `"tan"^ -1 (3/4) + "tan"^-1 (1/7)` is ____________.
`"tan"^-1 1 + "cos"^-1 ((-1)/2) + "sin"^-1 ((-1)/2)`
If `"cot"^-1 (sqrt"cos" alpha) - "tan"^-1 (sqrt"cos" alpha) = "x",` the sinx is equal to ____________.
`"cot" ("cosec"^-1 5/3 + "tan"^-1 2/3) =` ____________.
`"tan" (pi/4 + 1/2 "cos"^-1 "x") + "tan" (pi/4 - 1/2 "cos"^-1 "x") =` ____________.
The value of `"cos"^-1 ("cos" ((33pi)/5))` is ____________.
`"sin"^-1 (1 - "x") - 2 "sin"^-1 "x" = pi/2`
`"sin"^-1 ((-1)/2)`
`tan^-1 1/2 + tan^-1 2/11` is equal to
The Simplest form of `cot^-1 (1/sqrt(x^2 - 1))`, |x| > 1 is
`50tan(3tan^-1(1/2) + 2cos^-1(1/sqrt(5))) + 4sqrt(2) tan(1/2tan^-1(2sqrt(2)))` is equal to ______.
