Advertisements
Advertisements
Question
Show that `"sin"^-1(5/13) + "cos"^-1(3/5) = "tan"^-1(63/16)`
Solution
Let `"sin"^-1 (5/13) = "A" => "sin""A" = 5/13`
`therefore "cos""A" = sqrt(1-"sin"^2"A") = sqrt(1-(5/13)^2)`
`sqrt (1-25/169) = sqrt(144/169) = 12/13`
`=> "tan""A" = 5/12`
let `"cos"^-1(3/5) = "B" => "cos""B" = 3/5 `
sin B =`sqrt(1-9/25) = sqrt (16/25) = 4/5`
`therefore "tan""B" = 4/3`
Now , tan (A + B) =` ("tan""A" +"tan""B")/(1 - "tan""A""tan " "B")`
`=> "A" + "B" = "tan"^-1 [[ 5/12 +4/3]/(1-5/12 xx 4/3)]`
`= "tan"^-1 [[(5+16]/12)/( (36 - 20)/36]]`
A +B = `"tan"^-1 [(21/16)/3]`
`=> "sin"^-1 (5/13) + "cos"^-1(3/5) = "tan"^-1(63/16)`
= R.H.S
APPEARS IN
RELATED QUESTIONS
The principal solution of `cos^-1(-1/2)` is :
Write the principal value of `tan^(-1)+cos^(-1)(-1/2)`
Find the principal value of the following:
`sin^-1((sqrt3+1)/(2sqrt2))`
Find the principal value of the following:
`sin^-1(tan (5pi)/4)`
For the principal value, evaluate of the following:
`sin^-1(-1/2)+2cos^-1(-sqrt3/2)`
For the principal value, evaluate of the following:
`sin^-1(-sqrt3/2)+cos^-1(sqrt3/2)`
Find the principal value of the following:
`tan^-1(-1/sqrt3)`
For the principal value, evaluate of the following:
`tan^-1{2sin(4cos^-1 sqrt3/2)}`
Find the principal value of the following:
`sec^-1(-sqrt2)`
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)`
Find the principal value of the following:
`cosec^-1(-sqrt2)`
Find the principal value of the following:
`\text(cosec)^-1(2/sqrt3)`
Find the principal value of the following:
`cosec^-1(2cos (2pi)/3)`
For the principal value, evaluate the following:
`sin^-1(-sqrt3/2)+\text{cosec}^-1(-2/sqrt3)`
For the principal value, evaluate the following:
`sin^-1[cos{2\text(cosec)^-1(-2)}]`
Find the principal value of the following:
`cot^-1(-sqrt3)`
Find the principal value of the following:
`cot^-1(sqrt3)`
The index number by the method of aggregates for the year 2010, taking 2000 as the base year, was found to be 116. If sum of the prices in the year 2000 is ₹ 300, find the values of x and y in the data given below
| Commodity | A | B | C | D | E | F |
| Price in the year 2000 (₹) | 50 | x | 30 | 70 | 116 | 20 |
| Price in the year 2010 (₹) | 60 | 24 | y | 80 | 120 | 28 |
Find the principal value of cos–1x, for x = `sqrt(3)/2`.
Find the value of `tan^-1 (tan (9pi)/8)`.
Find the value of `sin[2cot^-1 ((-5)/12)]`
The principal value branch of sec–1 is ______.
The domain of sin–1 2x is ______.
The principal value of `sin^-1 ((-sqrt(3))/2)` is ______.
The value of `tan(cos^-1 3/5 + tan^-1 1/4)` is ______.
The value of the expression sin [cot–1 (cos (tan–11))] is ______.
Find the value of `4tan^-1 1/5 - tan^-1 1/239`
The value of `sin^-1 [cos((33pi)/5)]` is ______.
If `cos(sin^-1 2/5 + cos^-1x)` = 0, then x is equal to ______.
The value of the expression (cos–1x)2 is equal to sec2x.
The period of the function f(x) = cos4x + tan3x is ____________.
The general solution of the equation `"cot" theta - "tan" theta = "sec" theta` is ____________ where `(n in I).`
`2 "cos"^-1 "x = sin"^-1 (2"x" sqrt(1 - "x"^2))` is true for ____________.
`"sec" {"tan"^-1 (-"y"/3)}` is equal to ____________.
If `"tan"^-1 "x" + "tan"^-1"y + tan"^-1 "z" = pi/2, "x,y,x" > 0,` then the value of xy+yz+zx is ____________.
What is the principle value of `sin^-1 (1/sqrt(2))`?
