Advertisements
Advertisements
प्रश्न
The number of real solutions of the equation `sqrt(1 + cos 2x) = sqrt(2) cos^-1 (cos x)` in `[pi/2, pi]` is ______.
विकल्प
0
1
2
Infinite
उत्तर
The number of real solutions of the equation `sqrt(1 + cos 2x) = sqrt(2) cos^-1 (cos x)` in `[pi/2, pi]` is infinite.
Explanation:
We have `sqrt(1 + cos 2x) = sqrt(2) cos^-1 (cos x)`
⇒ `sqrt(2 cos^2x) = sqrt(2)x` .....`[because cos^-1 (cos x) = x]`
⇒ `sqrt(2) cos x = sqrt(2)x`
⇒ cos x = x
Which does not satisfy for any value of x.
APPEARS IN
संबंधित प्रश्न
If a line makes angles 90°, 60° and θ with x, y and z-axis respectively, where θ is acute, then find θ.
Write the following function in the simplest form:
`tan^(-1) (sqrt(1+x^2) -1)/x, x != 0`
Find the value of the following:
`tan^-1 [2 cos (2 sin^-1 1/2)]`
Find the value of the given expression.
`sin^(-1) (sin (2pi)/3)`
Prove that:
`cos^(-1) 4/5 + cos^(-1) 12/13 = cos^(-1) 33/65`
sin (tan–1 x), | x| < 1 is equal to ______.
Find the value, if it exists. If not, give the reason for non-existence
`sin^-1 [sin 5]`
Find the value of `sin^-1[cos(sin^-1 (sqrt(3)/2))]`
Solve: `cot^-1 x - cot^-1 (x + 2) = pi/12, x > 0`
Find the number of solutions of the equation `tan^-1 (x - 1) + tan^-1x + tan^-1(x + 1) = tan^-1(3x)`
Choose the correct alternative:
If `cot^-1(sqrt(sin alpha)) + tan^-1(sqrt(sin alpha))` = u, then cos 2u is equal to
Choose the correct alternative:
The equation tan–1x – cot–1x = `tan^-1 (1/sqrt(3))` has
Evaluate: `sin^-1 [cos(sin^-1 sqrt(3)/2)]`
Prove that `2sin^-1 3/5 - tan^-1 17/31 = pi/4`
Show that `2tan^-1 {tan alpha/2 * tan(pi/4 - beta/2)} = tan^-1 (sin alpha cos beta)/(cosalpha + sinbeta)`
Prove that `tan^-1 ((sqrt(1 + x^2) + sqrt(1 - x^2))/((1 + x^2) - sqrt(1 - x^2))) = pi/2 + 1/2 cos^-1x^2`
If a1, a2, a3,...,an is an arithmetic progression with common difference d, then evaluate the following expression.
`tan[tan^-1("d"/(1 + "a"_1 "a"_2)) + tan^-1("d"/(21 + "a"_2 "a"_3)) + tan^-1("d"/(1 + "a"_3 "a"_4)) + ... + tan^-1("d"/(1 + "a"_("n" - 1) "a""n"))]`
Solve for x : `"sin"^-1 2 "x" + sin^-1 3"x" = pi/3`
If `"tan"^-1 ("cot" theta) = 2theta, "then" theta` is equal to ____________.
`"cos" (2 "tan"^-1 1/7) - "sin" (4 "sin"^-1 1/3) =` ____________.
The value of `"tan"^-1 (1/2) + "tan"^-1(1/3) + "tan"^-1(7/8)` is ____________.
`"tan"^-1 1/3 + "tan"^-1 1/5 + "tan"^-1 1/7 + "tan"^-1 1/8 =` ____________.
`"cos"^-1 1/2 + 2 "sin"^-1 1/2` is equal to ____________.
The Government of India is planning to fix a hoarding board at the face of a building on the road of a busy market for awareness on COVID-19 protocol. Ram, Robert and Rahim are the three engineers who are working on this project. “A” is considered to be a person viewing the hoarding board 20 metres away from the building, standing at the edge of a pathway nearby. Ram, Robert and Rahim suggested to the firm to place the hoarding board at three different locations namely C, D and E. “C” is at the height of 10 metres from the ground level. For viewer A, the angle of elevation of “D” is double the angle of elevation of “C” The angle of elevation of “E” is triple the angle of elevation of “C” for the same viewer. Look at the figure given and based on the above information answer the following:
Measure of ∠DAB = ________.
The Government of India is planning to fix a hoarding board at the face of a building on the road of a busy market for awareness on COVID-19 protocol. Ram, Robert and Rahim are the three engineers who are working on this project. “A” is considered to be a person viewing the hoarding board 20 metres away from the building, standing at the edge of a pathway nearby. Ram, Robert and Rahim suggested to the firm to place the hoarding board at three different locations namely C, D and E. “C” is at the height of 10 metres from the ground level. For viewer A, the angle of elevation of “D” is double the angle of elevation of “C” The angle of elevation of “E” is triple the angle of elevation of “C” for the same viewer. Look at the figure given and based on the above information answer the following:
Domain and Range of tan-1 x = ________.
The value of `tan^-1 (x/y) - tan^-1 (x - y)/(x + y)` is equal to
Find the value of `tan^-1 [2 cos (2 sin^-1 1/2)] + tan^-1 1`.
Write the following function in the simplest form:
`tan^-1 ((cos x - sin x)/(cos x + sin x)), (-pi)/4 < x < (3 pi)/4`
