Advertisements
Advertisements
प्रश्न
Show that `sin^-1 5/13 + cos^-1 3/5 = tan^-1 63/16`
Advertisements
उत्तर
`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
संबंधित प्रश्न
If `sin^-1(1-x) -2sin^-1x = pi/2` then x is
- -1/2
- 1
- 0
- 1/2
Show that `2sin^-1(3/5) = tan^-1(24/7)`
Show that:
`cos^(-1)(4/5)+cos^(-1)(12/13)=cos^(-1)(33/65)`
Find the principal value of the following:
`cos^(-1) (-1/2)`
`sin^-1 1/2-2sin^-1 1/sqrt2`
`sin^-1{cos(sin^-1 sqrt3/2)}`
Evaluate the following:
`cot^-1 1/sqrt3-\text(cosec)^-1(-2)+sec^-1(2/sqrt3)`
Evaluate the following:
`cot^-1{2cos(sin^-1 sqrt3/2)}`
In ΔABC, if a = 18, b = 24, c = 30 then find the values of cosA
In ΔABC, if a = 18, b = 24, c = 30 then find the values of sin `(A/2)`.
Evaluate the following:
`tan^-1(1) + cos^-1(1/2) + sin^-1(1/2)`
Prove the following:
`sin^-1(3/5) + cos^-1(12/13) = sin^-1(56/65)`
Find the principal value of the following:
`sec^-1 (-sqrt2)`
Prove that:
`tan^-1 (4/3) + tan^-1 (1/7) = pi/4`
Solve `tan^-1 2x + tan^-1 3x = pi/4`
Evaluate: sin`[1/2 cos^-1 (4/5)]`
Express `tan^-1 [(cos x)/(1 - sin x)], - pi/2 < x < (3pi)/2` in the simplest form.
The principle solutions of equation tan θ = -1 are ______
The principal value of `tan^{-1(sqrt3)}` is ______
The equation tan–1x – cot–1x = `(1/sqrt(3))` has ______.
If `"sin"^-1("x"^2 - 7"x" + 12) = "n"pi, AA "n" in "I"`, then x = ____________.
`"cos"^-1 1/2 + 2 "sin"^-1 1/2` is equal to ____________.
3 tan-1 a is equal to ____________.
`"tan"^-1 sqrt3 - "sec"^-1 (-2)` is equal to ____________.
The equation of the tangent to the curve given by x = a sin3t, y = bcos3t at a point where t = `pi/2` is
Which of the following functions is inverse of itself?
Domain and Rariges of cos–1 is:-
What will be the principal value of `sin^-1(-1/2)`?
what is the value of `cos^-1 (cos (13pi)/6)`
What is the values of `cos^-1 (cos (7pi)/6)`
If `sin(sin^-1 1/5 + cos^-1 x) = 1`, the what will be the value of x?
If f'(x) = x–1, then find f(x)
Let x = sin–1(sin8) + cos–1(cos11) + tan–1(tan7), and x = k(π – 2.4) for an integer k, then the value of k is ______.
`(tan^-1 (sqrt(3)) - sec^-1(-2))/("cosec"^-1(-sqrt(2)) + cos^-1(-1/2))` is equal to ______.
If cos–1 x > sin–1 x, then ______.
Find the value of `tan^-1(x/y) + tan^-1((y - x)/(y + x))`
