Advertisements
Advertisements
Question
Show that `sin^-1 5/13 + cos^-1 3/5 = tan^-1 63/16`
Solution
`sin^-1 5/13 = tan^-1 5/12`
`cos^-1 3/5 = tan^-1 4/3`
∴ L.H.S. = `sin^-1 5/13 + cos^-1 3/5`
= `tan^-1 5/12 + tan^-1 4/3`
= `tan-1 (5/12 + 4/3)/(1 - 5/12 * 4/3)`
= `tan^-1 ((15 + 48)/36)/((36 - 20)/36)`
= `tan^-1 63/16`
APPEARS IN
RELATED QUESTIONS
Find the principal value of `cos^(-1) (-1/2)`
Find the value of the following:
`tan^(-1) (tan (7x)/6)`
Find the set of values of `cosec^-1(sqrt3/2)`
Find the domain of `f(x)=cotx+cot^-1x`
Solve for x:
`tan^-1 [(x-1),(x-2)] + tan^-1 [(x+1),(x+2)] = x/4`
In ΔABC, if a = 18, b = 24, c = 30 then find the values of tan `A/2`
In ΔABC, if a = 18, b = 24, c = 30 then find the values of A(ΔABC)
In ΔABC prove that `sin "A"/(2). sin "B"/(2). sin "C"/(2) = ["A(ΔABC)"]^2/"abcs"`
Prove the following:
`cos^-1(3/5) + cos^-1(4/5) = pi/(2)`
sin−1x − cos−1x = `pi/6`, then x = ______
Prove that cot−1(7) + 2 cot−1(3) = `pi/4`
Show that `sin^-1(3/5) + sin^-1(8/17) = cos^-1(36/85)`
Find the principal value of the following:
cosec-1 (2)
Prove that:
`tan^-1 (4/3) + tan^-1 (1/7) = pi/4`
Solve: tan-1 (x + 1) + tan-1 (x – 1) = `tan^-1 (4/7)`
If `sin^-1(x/13) + cosec^-1(13/12) = pi/2`, then the value of x is ______
The principal value of `tan^{-1(sqrt3)}` is ______
If `3sin^-1((2x)/(1 + x^2)) - 4cos^-1((1 - x^2)/(1 + x^2)) + 2tan^-1((2x)/(1 - x^2)) = pi/3`, then x is equal to ______
If `tan^-1x + tan^-1y = (4pi)/5`, then `cot^-1x + cot^-1y` equals ______.
`cos^-1 4/5 + tan^-1 3/5` = ______.
Solve for x `tan^-1((1 - x)/(1 + x)) = 1/2 tan^-1x, x > 0`
The domain of the function defined by f(x) = sin–1x + cosx is ______.
`"sin"^-1 (1/sqrt2)`
`2"tan"^-1 ("cos x") = "tan"^-1 (2 "cosec x")`
If a = `(2sin theta)/(1 + costheta + sintheta)`, then `(1 + sintheta - costheta)/(1 + sintheta)` is
Value of `sin(pi/3 - sin^1 (- 1/2))` is equal to
Number of values of x satisfying the system of equations `sin^-1sqrt(2 + e^(-2x) - 2e^-x) + sec^-1sqrt(1 - x^2 + x^4) = π/2` and `5^(1+tan^-1x)` = 4 + [cos–1x] is ______ (where [.] denotes greatest integer function)
cos–1(cos10) is equal to ______.
If sin–1a + sin–1b + sin–1c = π, then find the value of `asqrt(1 - a^2) + bsqrt(1 - b^2) + csqrt(1 - c^2)`.
