Advertisements
Advertisements
प्रश्न
The value of the expression (cos–1x)2 is equal to sec2x.
विकल्प
True
False
Advertisements
उत्तर
This statement is False.
Explanation:
We know that `cos^-1x = sec^-1 (1/x) ≠ sec x`
So `(cos^-1x)^2 ≠ sec^2x`
APPEARS IN
संबंधित प्रश्न
Prove that `sin^(-1) (3/5) + cos^(-1) (12/13) = sin^(-1) (56/65)`
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(-1/sqrt3)`
For the principal value, evaluate the following:
`tan^-1sqrt3-sec^-1(-2)`
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(-sqrt3/2)+\text{cosec}^-1(-2/sqrt3)`
For the principal value, evaluate the following:
`cosec^-1(2tan (11pi)/6)`
Find the principal value of the following:
`cot^-1(tan (3pi)/4)`
If `sin^-1"x" + tan^-1"x" = pi/2`, prove that `2"x"^2 + 1 = sqrt5`
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 `cos^-1(cos (13pi)/6)`.
Find the value of `tan^-1 (tan (9pi)/8)`.
Prove that tan(cot–1x) = cot(tan–1x). State with reason whether the equality is valid for all values of x.
Find the values of x which satisfy the equation sin–1x + sin–1(1 – x) = cos–1x.
The value of `sin^-1 (cos((43pi)/5))` is ______.
The principal value of the expression cos–1[cos (– 680°)] is ______.
The value of cot (sin–1x) is ______.
The domain of sin–1 2x is ______.
The value of tan2 (sec–12) + cot2 (cosec–13) is ______.
Find the value of `tan^-1 (tan (5pi)/6) +cos^-1(cos (13pi)/6)`
Find the value of `tan^-1 (tan (2pi)/3)`
Find the value of the expression `sin(2tan^-1 1/3) + cos(tan^-1 2sqrt(2))`
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 principal value of `cos^-1 (- 1/2)` is ______.
The set of values of `sec^-1 (1/2)` is ______.
The principal value of `tan^-1 sqrt(3)` is ______.
The result `tan^1x - tan^-1y = tan^-1 ((x - y)/(1 + xy))` is true when value of xy is ______.
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.
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)`.
