Advertisements
Advertisements
Question
Find the principal value of the following:
`sin^-1(cos (3pi)/4)`
Solution
`sin^-1(cos (3pi)/4) = sin^-1(-sqrt2/2)=sin^-1[sin(-pi/4)]=-pi/4`
APPEARS IN
RELATED QUESTIONS
Write the principal value of `tan^(-1)+cos^(-1)(-1/2)`
The principal solution of the equation cot x=`-sqrt 3 ` is
if `tan^(-1) a + tan^(-1) b + tan^(-1) x = pi`, prove that a + b + c = abc
Find the principal value of the following:
`sin^-1(cos (2pi)/3)`
Find the principal value of the following:
`tan^-1(1/sqrt3)`
Find the principal value of the following:
`tan^-1(2cos (2pi)/3)`
Find the principal value of the following:
`sec^-1(-sqrt2)`
Find the principal value of the following:
`cosec^-1(-sqrt2)`
Find the principal value of the following:
`cosec^-1(2cos (2pi)/3)`
For the principal value, evaluate the following:
`sin^-1[cos{2\text(cosec)^-1(-2)}]`
For the principal value, evaluate the following:
`cosec^-1(2tan (11pi)/6)`
Find the principal value of the following:
`cot^-1(sqrt3)`
Find the principal value of the following:
`cot^-1(tan (3pi)/4)`
Find the principal value of cos–1x, for x = `sqrt(3)/2`.
Prove that tan(cot–1x) = cot(tan–1x). State with reason whether the equality is valid for all values of x.
The principal value branch of sec–1 is ______.
The value of `sin^-1 (cos((43pi)/5))` is ______.
The greatest and least values of (sin–1x)2 + (cos–1x)2 are respectively ______.
If sin–1x + sin–1y = `pi/2`, then value of cos–1x + cos–1y is ______.
The value of `sin^-1 [cos((33pi)/5)]` is ______.
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 the expression `2 sec^-1 2 + sin^-1 (1/2)` is ______.
If `cos(tan^-1x + cot^-1 sqrt(3))` = 0, then value of x is ______.
The principal value of `tan^-1 sqrt(3)` is ______.
The value of `cos^-1 (cos (14pi)/3)` is ______.
The value of expression `tan((sin^-1x + cos^-1x)/2)`, when x = `sqrt(3)/2` is ______.
The value of the expression (cos–1x)2 is equal to sec2x.
The least numerical value, either positive or negative of angle θ is called principal value of the inverse trigonometric function.
The minimum value of n for which `tan^-1 "n"/pi > pi/4`, n ∈ N, is valid is 5.
If `5 sin theta = 3 "then", (sec theta + tan theta)/(sec theta - tan theta)` is equal to ____________.
The period of the function f(x) = cos4x + tan3x is ____________.
`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 ____________.
Which of the following is the principal value branch of `"cos"^-1 "x"`
What is the principal value of `cot^-1 ((-1)/sqrt(3))`?
Evaluate `sin^-1 (sin (3π)/4) + cos^-1 (cos π) + tan^-1 (1)`.