Advertisements
Advertisements
Question
Find the value of `cot[sin^-1 3/5 + sin^-1 4/5]`
Solution
`cot[sin^-1 3/5 + sin^-1 4/5]`
= `cot [sin^-1 (3/5 sqrt(1 - (4/5)^2) + 4/5 sqrt(1 - (3/5)^2))]`
= `cot[sin^-1 (3/5 sqrt(1 - 16/25) + 4/5 sqrt(1 - 9/25))]`
= `cot [sin^-1 (3/5 sqrt(9/25) + 4/5 sqrt(16/25))]`
= `cot [sin^-1 (3/5 xx 3/5 + 4/5 xx 4/5)]`
= `cot[sin^-1 (9/25 + 16/25)]`
= `cot[sin^-1 (25/25)]`
= `cot [sin^-1(1)]`
= `cot pi/2`
= 0
APPEARS IN
RELATED QUESTIONS
Prove that `cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=x/2;x in (0,pi/4) `
Write the function in the simplest form: `tan^(-1) 1/(sqrt(x^2 - 1)), |x| > 1`
Find the value of the following:
`tan^-1 [2 cos (2 sin^-1 1/2)]`
Find the value of the given expression.
`sin^(-1) (sin (2pi)/3)`
`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 `tan {pi/4 + 1/2 cos^(-1) a/b} + tan {pi/4 - 1/2 cos^(-1) a/b} = (2b)/a`
Solve for x : \[\tan^{- 1} \left( \frac{x - 2}{x - 1} \right) + \tan^{- 1} \left( \frac{x + 2}{x + 1} \right) = \frac{\pi}{4}\] .
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)`.
Prove that `2sin^-1 3/5 - tan^-1 17/31 = pi/4`
Show that `2tan^-1 {tan alpha/2 * tan(pi/4 - beta/2)} = tan^-1 (sin alpha cos beta)/(cosalpha + sinbeta)`
Prove that `sin^-1 8/17 + sin^-1 3/5 = sin^-1 7/85`
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"))]`
If 3 tan–1x + cot–1x = π, then x equals ______.
If cos–1x > sin–1x, then ______.
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`
The value of `"tan"^ -1 (3/4) + "tan"^-1 (1/7)` is ____________.
If `"sin" {"sin"^-1 (1/2) + "cos"^-1 "x"} = 1`, then the value of x is ____________.
