Advertisements
Advertisements
प्रश्न
Solve the following equation for x: `cos (tan^(-1) x) = sin (cot^(-1) 3/4)`
Advertisements
उत्तर
The given equation is `cos (tan^(-1) x) = sin (cot^(-1) 3/4)`
`cos (tan^(-1) x) = sin(cot^(-1) 3/4)`
`=> cos (tan^(-1) x) = cos(pi/2 - cot^(-1) 3 /4)` `[sintheta = cos(pi/2 - theta)]`
`=> cos(tan^(-1) x) = cos(tan^(-1) (3/4))` `(tan^(-1) x + cot^(-1) x = pi/2)`
`=> tan^(-1) x = tan^(-1) (3/4)`
`=> x = 3/4`
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 function in the simplest form: `tan^(-1) 1/(sqrt(x^2 - 1)), |x| > 1`
Write the following function in the simplest form:
`tan^(-1) x/(sqrt(a^2 - x^2))`, |x| < a
Find the value of the following:
`tan 1/2 [sin^(-1) (2x)/(1+ x^2) + cos^(-1) (1-y^2)/(1+y^2)]`, |x| < 1, y > 0 and xy < 1
Prove that:
`tan^(-1) sqrtx = 1/2 cos^(-1) (1-x)/(1+x)`, x ∈ [0, 1]
sin (tan–1 x), |x| < 1 is equal to ______.
sin–1 (1 – x) – 2 sin–1 x = `pi/2`, then x is equal to ______.
If y = `(x sin^-1 x)/sqrt(1 -x^2)`, prove that: `(1 - x^2)dy/dx = x + y/x`
Solve: tan-1 4 x + tan-1 6x `= π/(4)`.
Solve: `2tan^-1 (cos x) = tan^-1 (2"cosec" x)`
Choose the correct alternative:
sin–1(2 cos2x – 1) + cos–1(1 – 2 sin2x) =
Evaluate tan (tan–1(– 4)).
Show that `2tan^-1 {tan alpha/2 * tan(pi/4 - beta/2)} = tan^-1 (sin alpha cos beta)/(cosalpha + sinbeta)`
Evaluate `cos[cos^-1 ((-sqrt(3))/2) + pi/6]`
The value of the expression `tan (1/2 cos^-1 2/sqrt(5))` is ______.
If |x| ≤ 1, then `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))` is equal to ______.
The minimum value of sinx - cosx is ____________.
The value of `"tan"^ -1 (3/4) + "tan"^-1 (1/7)` is ____________.
`"cot" (pi/4 - 2 "cot"^-1 3) =` ____________.
`"cos" (2 "tan"^-1 1/7) - "sin" (4 "sin"^-1 1/3) =` ____________.
If `"tan"^-1 (("x" - 1)/("x" + 2)) + "tan"^-1 (("x" + 1)/("x" + 2)) = pi/4,` then x is equal to ____________.
sin (tan−1 x), where |x| < 1, is equal to:
The value of `"tan"^-1 (1/2) + "tan"^-1(1/3) + "tan"^-1(7/8)` is ____________.
If `"tan"^-1 2 "x + tan"^-1 3 "x" = pi/4`, then x is ____________.
The value of `"cos"^-1 ("cos" ((33pi)/5))` is ____________.
If `"sin"^-1 (1 - "x") - 2 "sin"^-1 ("x") = pi/2,` then x is equal to ____________.
Solve for x : `{"x cos" ("cot"^-1 "x") + "sin" ("cot"^-1 "x")}^2` = `51/50
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 ∠EAB = ________.
`tan^-1 1/2 + tan^-1 2/11` is equal to
The set of all values of k for which (tan–1 x)3 + (cot–1 x)3 = kπ3, x ∈ R, is the internal ______.
