Advertisements
Advertisements
प्रश्न
Write the principal value of `tan^(-1)+cos^(-1)(-1/2)`
उत्तर
`Let tan^(-1)=y and cos^(-1)(-1/2)=z`
`tany=1=tan(pi/4) and cosz=-1/2=-cos(pi/3)=cos(pi-pi/3)=cos((2pi)/3)`
The ranges of principal value branch of tan−1 and cos−1 are `(-pi/2,pi/2)and[0,pi] ` respectively
`therefore tan^(-1)=pi/4 and cos^(-1)(-1/2)=2pi/3`
`therefore tan^(-1)(1)+cos^(-1)(-1/2)=pi/4+(2pi)/3=(11pi)/12`
APPEARS IN
संबंधित प्रश्न
The principal solution of `cos^-1(-1/2)` is :
The principal solution of the equation cot x=`-sqrt 3 ` is
Find the principal value of the following:
`sin^-1((sqrt3+1)/(2sqrt2))`
Find the principal value of the following:
`sin^-1(cos (3pi)/4)`
Find the principal value of the following:
`tan^-1(2cos (2pi)/3)`
For the principal value, evaluate of the following:
`tan^-1(-1)+cos^-1(-1/sqrt2)`
For the principal value, evaluate of the following:
`tan^-1{2sin(4cos^-1 sqrt3/2)}`
For the principal value, evaluate the following:
`tan^-1sqrt3-sec^-1(-2)`
For the principal value, evaluate the following:
`sin^-1(-sqrt3/2)-2sec^-1(2tan pi/6)`
Find the principal value of the following:
`cosec^-1(-sqrt2)`
Find the principal value of the following:
cosec-1(-2)
For the principal value, evaluate the following:
`sec^-1(sqrt2)+2\text{cosec}^-1(-sqrt2)`
Show that `"sin"^-1(5/13) + "cos"^-1(3/5) = "tan"^-1(63/16)`
Find the principal value of cos–1x, for x = `sqrt(3)/2`.
Find the value of `sec(tan^-1 y/2)`
Find the value of `sin(2tan^-1 2/3) + cos(tan^-1 sqrt(3))`
The principal value of the expression cos–1[cos (– 680°)] is ______.
The value of cot (sin–1x) is ______.
The value of sin (2 sin–1 (.6)) is ______.
Find the value of `tan^-1 (- 1/sqrt(3)) + cot^-1(1/sqrt(3)) + tan^-1(sin((-pi)/2))`
The value of sin (2 tan–1(0.75)) is equal to ______.
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.
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 ____________.
`"cos" ["tan"^-1 {"sin" ("cot"^-1 "x")}]` is equal to ____________.
If `"tan"^-1 ("a"/"x") + "tan"^-1 ("b"/"x") = pi/2,` then x is equal to ____________.
What is the value of x so that the seven-digit number 8439 × 53 is divisible by 99?
What is the value of `tan^-1(1) cos^-1(- 1/2) + sin^-1(- 1/2)`
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]`.
Evaluate `sin^-1 (sin (3π)/4) + cos^-1 (cos π) + tan^-1 (1)`.
