Advertisements
Advertisements
Question
Solve: `sin^-1 5/x + sin^-1 12/x = pi/2`
Solution
`sin^-1 5/x = pi/2 - sin^1 12/x`
`pi/2 - (cos^-1 5/x) = pi/2 - sin^-1 12/x`
`cos^-1 5/x = sin^-1 12/x`
cos θ = `5/x`
sin θ = `12/x`
`sin^2theta + cos^2theta` = 1
`(5/x)^2 + (12/x)^2` = 1
`25/x + 144/x^2` = 1
`169/x^2` = 1
x2 = 169
⇒ x = `+- 13`
APPEARS IN
RELATED QUESTIONS
Prove the following:
`3cos^(-1) x = cos^(-1)(4x^3 - 3x), x in [1/2, 1]`
Prove `2 tan^(-1) 1/2 + tan^(-1) 1/7 = tan^(-1) 31/17`
Write the function in the simplest form: `tan^(-1) ((cos x - sin x)/(cos x + sin x)) `,` 0 < x < pi`
`cos^(-1) (cos (7pi)/6)` is equal to ______.
`sin[pi/3 - sin^(-1) (-1/2)]` is equal to ______.
If cos-1 x + cos -1 y + cos -1 z = π , prove that x2 + y2 + z2 + 2xyz = 1.
Find: ∫ sin x · log cos x dx
Prove that `tan^-1 2/11 + tan^-1 7/24 = tan^-1 1/2`
Solve the equation `sin^-1 6x + sin^-1 6sqrt(3)x = - pi/2`
If cos–1α + cos–1β + cos–1γ = 3π, then α(β + γ) + β(γ + α) + γ(α + β) equals ______.
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 (3/4) + "tan"^-1 (1/7)` 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 ____________.
`"cot" ("cosec"^-1 5/3 + "tan"^-1 2/3) =` ____________.
sin (tan−1 x), where |x| < 1, is equal to:
If `3 "sin"^-1 ((2"x")/(1 + "x"^2)) - 4 "cos"^-1 ((1 - "x"^2)/(1 + "x"^2)) + 2 "tan"^-1 ((2"x")/(1 - "x"^2)) = pi/3` then x is equal to ____________.
`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 ______.
If `cos^-1(2/(3x)) + cos^-1(3/(4x)) = π/2(x > 3/4)`, then x is equal to ______.
