Advertisements
Advertisements
Question
Solve: `sin^-1 5/x + sin^-1 12/x = pi/2`
Advertisements
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
Find the value of the following:
`tan^-1 [2 cos (2 sin^-1 1/2)]`
Prove that:
`tan^(-1) 63/16 = sin^(-1) 5/13 + cos^(-1) 3/5`
Find: ∫ sin x · log cos x dx
Solve for x : `tan^-1 ((2-"x")/(2+"x")) = (1)/(2)tan^-1 ("x")/(2), "x">0.`
Find the value, if it exists. If not, give the reason for non-existence
`sin^-1 [sin 5]`
Solve: `2tan^-1 (cos x) = tan^-1 (2"cosec" x)`
Prove that cot–17 + cot–18 + cot–118 = cot–13
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 `"cot"^-1 (sqrt"cos" alpha) - "tan"^-1 (sqrt"cos" alpha) = "x",` the sinx is equal to ____________.
The value of cot `("cosec"^-1 5/3 + "tan"^-1 2/3)` is ____________.
`"tan"^-1 1/3 + "tan"^-1 1/5 + "tan"^-1 1/7 = "tan"^-1 1/8 =` ____________.
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 ____________.
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") =` ____________.
`"sin"^-1 (1 - "x") - 2 "sin"^-1 "x" = pi/2`
`tan^-1 1/2 + tan^-1 2/11` is equal to
If sin–1x + sin–1y + sin–1z = π, show that `x^2 - y^2 - z^2 + 2yzsqrt(1 - x^2) = 0`
