Advertisements
Advertisements
प्रश्न
If a line makes angles 90°, 60° and θ with x, y and z-axis respectively, where θ is acute, then find θ.
Advertisements
उत्तर
We have
α=90°
β=60°
γ=θ
Since cos2α+cos2β+cos2γ=1,
`cos^2(90°)+cos^2(60°)+cos^2θ=1 `
`0^2+(1/2)^2+cos^2θ=1`
`cos^2θ=1−1/4=3/4`
`cosθ=sqrt3/2 (θ is acute.)`
`∴ θ=30°`
APPEARS IN
संबंधित प्रश्न
Prove the following:
3cos–1x = cos–1 (4x3 – 3x), `x ∈ [1/2, 1]`
Write the following function in the simplest form:
`tan^(-1) x/(sqrt(a^2 - x^2)), |x| < a`
if `sin(sin^(-1) 1/5 + cos^(-1) x) = 1` then find the value of x
Prove that `cos^(-1) 12/13 + sin^(-1) 3/5 = sin^(-1) 56/65`.
Prove `tan^(-1) 1/5 + tan^(-1) (1/7) + tan^(-1) 1/3 + tan^(-1) 1/8 = pi/4`
Solve `tan^(-1) - tan^(-1) (x - y)/(x+y)` is equal to
(A) `pi/2`
(B). `pi/3`
(C) `pi/4`
(D) `(-3pi)/4`
Prove that `tan^-1 2/11 + tan^-1 7/24 = tan^-1 1/2`
Prove that `tan^-1x + tan^-1 (2x)/(1 - x^2) = tan^-1 (3x - x^3)/(1 - 3x^2), |x| < 1/sqrt(3)`
Solve: `cot^-1 x - cot^-1 (x + 2) = pi/12, x > 0`
Choose the correct alternative:
`tan^-1 (1/4) + tan^-1 (2/9)` is equal to
Choose the correct alternative:
sin–1(2 cos2x – 1) + cos–1(1 – 2 sin2x) =
Prove that cot–17 + cot–18 + cot–118 = cot–13
Evaluate `cos[cos^-1 ((-sqrt(3))/2) + pi/6]`
If |x| ≤ 1, then `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))` is equal to ______.
If cos–1α + cos–1β + cos–1γ = 3π, then α(β + γ) + β(γ + α) + γ(α + β) equals ______.
The minimum value of sinx - cosx is ____________.
`"cot" (pi/4 - 2 "cot"^-1 3) =` ____________.
sin (tan−1 x), where |x| < 1, is equal to:
The value of `"tan"^-1 (3/4) + "tan"^-1 (1/7)` is ____________.
`"cos"^-1["cos"(2"cot"^-1(sqrt2 - 1))]` = ____________.
If `6"sin"^-1 ("x"^2 - 6"x" + 8.5) = pi,` then x is equal to ____________.
`"cos"^-1 1/2 + 2 "sin"^-1 1/2` is equal to ____________.
`"sin"^-1 (1/sqrt2)`
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 ∠CAB = ________.
`sin^-1(1 - x) - 2sin^-1 x = pi/2`, tan 'x' is equal to
`50tan(3tan^-1(1/2) + 2cos^-1(1/sqrt(5))) + 4sqrt(2) tan(1/2tan^-1(2sqrt(2)))` is equal to ______.
The value of cosec `[sin^-1((-1)/2)] - sec[cos^-1((-1)/2)]` is equal to ______.
