Advertisements
Advertisements
प्रश्न
Prove that `sin^(-1) (3/5) + cos^(-1) (12/13) = sin^(-1) (56/65)`
उत्तर
Let `cos^(-1) 12/13 = x`
∴ `cos x = 12/13`
∴ `sin x = 5/13`
and let `sin^(-1) 3/5 = y `
sin y = `3/5`
`:. cos y= 4/5`
∴ using sin (x + y) = sin x cos y + cos x sin y
`= 5/13xx4/5+ 12/13xx3/5`
`= (20+36)/(13xx5)`
= `56/65`
∴ x + y =`sin^(-1) 56/65`
`cos^(-1) 12/13 + sin^(-1) 3/5 = sin^(-1) 56/65`
Hence proved.
APPEARS IN
संबंधित प्रश्न
Find the value of `tan^(-1) sqrt3 - cot^(-1) (-sqrt3)`
Find the principal value of the following:
`sin^-1(-sqrt3/2)`
Find the principal value of the following:
`sin^-1(cos (2pi)/3)`
Find the principal value of the following:
`sin^-1((sqrt3+1)/(2sqrt2))`
For the principal value, evaluate of the following:
`cos^-1 1/2+2sin^-1 (1/2)`
Find the principal value of the following:
`tan^-1(cos pi/2)`
Find the principal value of the following:
`sec^-1(2)`
Find the principal value of the following:
`sec^-1(2sin (3pi)/4)`
Find the principal value of the following:
`sec^-1(2tan (3pi)/4)`
For the principal value, evaluate the following:
`sec^-1(sqrt2)+2\text{cosec}^-1(-sqrt2)`
For the principal value, evaluate the following:
`sin^-1[cos{2\text(cosec)^-1(-2)}]`
if sec-1 x = cosec-1 v. show that `1/x^2 + 1/y^2 = 1`
Solve for x, if:
tan (cos-1x) = `2/sqrt5`
If `sin^-1"x" + tan^-1"x" = pi/2`, prove that `2"x"^2 + 1 = sqrt5`
Find value of tan (cos–1x) and hence evaluate `tan(cos^-1 8/17)`
Find the value of `sin[2cot^-1 ((-5)/12)]`
Find the values of x which satisfy the equation sin–1x + sin–1(1 – x) = cos–1x.
The principal value branch of sec–1 is ______.
One branch of cos–1 other than the principal value branch corresponds to ______.
The value of cot (sin–1x) is ______.
Find the value of `4tan^-1 1/5 - tan^-1 1/239`
The domain of the function defined by f(x) = `sin^-1 sqrt(x- 1)` is ______.
If `cos(sin^-1 2/5 + cos^-1x)` = 0, then x is equal to ______.
The value of sin (2 tan–1(0.75)) is equal to ______.
The value of the expression `2 sec^-1 2 + sin^-1 (1/2)` is ______.
If tan–1x + tan–1y = `(4pi)/5`, then cot–1x + cot–1y equals ______.
The set of values of `sec^-1 (1/2)` is ______.
The principal value of `tan^-1 sqrt(3)` is ______.
The domain of trigonometric functions can be restricted to any one of their branch (not necessarily principal value) in order to obtain their inverse functions.
If `5 sin theta = 3 "then", (sec theta + tan theta)/(sec theta - tan theta)` is equal to ____________.
`2 "cos"^-1 "x = sin"^-1 (2"x" sqrt(1 - "x"^2))` is true for ____________.
If sin `("sin"^-1 1/5 + "cos"^-1 "x") = 1,` then the value of x is ____________.
What is the principal value of `cot^-1 ((-1)/sqrt(3))`?
Assertion (A): Maximum value of (cos–1 x)2 is π2.
Reason (R): Range of the principal value branch of cos–1 x is `[(-π)/2, π/2]`.
