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 ______.
पर्याय
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
Prove that: `tan^(-1)(1/2)+tan^(-1)(1/5)+tan^(-1)(1/8)=pi/4`
Prove that:
`tan^(-1)""1/5+tan^(-1)""1/7+tan^(-1)""1/3+tan^(-1)""1/8=pi/4`
Write the function in the simplest form: `tan^(-1) ((cos x - sin x)/(cos x + sin x)) `,` 0 < x < pi`
Write the following function in the simplest form:
`tan^(-1) x/(sqrt(a^2 - x^2))`, |x| < a
if `tan^(-1) (x-1)/(x - 2) + tan^(-1) (x + 1)/(x + 2) = pi/4` then find the value of x.
Prove that `tan {pi/4 + 1/2 cos^(-1) a/b} + tan {pi/4 - 1/2 cos^(-1) a/b} = (2b)/a`
Solve for x : `tan^-1 ((2-"x")/(2+"x")) = (1)/(2)tan^-1 ("x")/(2), "x">0.`
Find the value of the expression in terms of x, with the help of a reference triangle
`tan(sin^-1(x + 1/2))`
Find the number of solutions of the equation `tan^-1 (x - 1) + tan^-1x + tan^-1(x + 1) = tan^-1(3x)`
Evaluate: `tan^-1 sqrt(3) - sec^-1(-2)`.
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`
Prove that `sin^-1 8/17 + sin^-1 3/5 = sin^-1 7/85`
The maximum value of sinx + cosx is ____________.
The value of `"tan"^-1 (1/2) + "tan"^-1 (1/3) + "tan"^-1 (7/8)` is ____________.
If `"tan"^-1 ("cot" theta) = 2theta, "then" theta` is equal to ____________.
`"cot" ("cosec"^-1 5/3 + "tan"^-1 2/3) =` ____________.
sin (tan−1 x), where |x| < 1, is equal to:
Solve for x : `"sin"^-1 2"x" + "sin"^-1 3"x" = pi/3`
`"cos" (2 "tan"^-1 1/7) - "sin" (4 "sin"^-1 1/3) =` ____________.
`"sin"^-1 (1 - "x") - 2 "sin"^-1 "x" = pi/2`
`"tan"^-1 (sqrt3)`
If `"sin" {"sin"^-1 (1/2) + "cos"^-1 "x"} = 1`, then the value of x is ____________.
If `3 "sin"^-1 ((2"x")/(1 + "x"^2)) - 4 "cos"^-1 ((1 - "x"^2)/(1 + "x"^2)) + 2 "tan"^-1 ((2"x")/(1 - "x"^2)) = pi/3` then x 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:
𝐴' Is another viewer standing on the same line of observation across the road. If the width of the road is 5 meters, then the difference between ∠CAB and ∠CA'B is ______.
Find the value of `cos^-1 (1/2) + 2sin^-1 (1/2) ->`:-
The value of cosec `[sin^-1((-1)/2)] - sec[cos^-1((-1)/2)]` is equal to ______.
Solve for x: `sin^-1(x/2) + cos^-1x = π/6`
Solve:
sin–1(x) + sin–1(1 – x) = cos–1x.
