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प्रश्न
The value of the expression (cos–1x)2 is equal to sec2x.
विकल्प
True
False
उत्तर
This statement is False.
Explanation:
We know that `cos^-1x = sec^-1 (1/x) ≠ sec x`
So `(cos^-1x)^2 ≠ sec^2x`
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संबंधित प्रश्न
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(-sqrt3/2)`
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)`
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(cos pi/2)`
Find the principal value of the following:
`sec^-1(2sin (3pi)/4)`
Find the principal value of the following:
cosec-1(-2)
Find the principal value of the following:
`\text(cosec)^-1(2/sqrt3)`
For the principal value, evaluate the following:
`sec^-1(sqrt2)+2\text{cosec}^-1(-sqrt2)`
Find the principal value of the following:
`cot^-1(-sqrt3)`
Find the principal value of the following:
`cot^-1(tan (3pi)/4)`
Show that `"sin"^-1(5/13) + "cos"^-1(3/5) = "tan"^-1(63/16)`
Find the value of `cos^-1(cos (13pi)/6)`.
Find the value of `tan^-1 (tan (9pi)/8)`.
Which of the following corresponds to the principal value branch of tan–1?
The domain of the function cos–1(2x – 1) is ______.
If `cos(sin^-1 2/5 + cos^-1x)` = 0, then x is equal to ______.
If tan–1x + tan–1y = `(4pi)/5`, then cot–1x + cot–1y equals ______.
The value of `cot[cos^-1 (7/25)]` is ______.
The principal value of `tan^-1 sqrt(3)` is ______.
The value of `cos^-1 (cos (14pi)/3)` is ______.
The value of cos (sin–1x + cos–1x), |x| ≤ 1 is ______.
The value of expression `tan((sin^-1x + cos^-1x)/2)`, when x = `sqrt(3)/2` 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.
The minimum value of n for which `tan^-1 "n"/pi > pi/4`, n ∈ N, is valid is 5.
The principal value of `sin^-1 [cos(sin^-1 1/2)]` is `pi/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]`.
