Advertisements
Advertisements
Question
If a line makes angles 90°, 60° and θ with x, y and z-axis respectively, where θ is acute, then find θ.
Solution
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
RELATED QUESTIONS
Prove `tan^(-1) 2/11 + tan^(-1) 7/24 = tan^(-1) 1/2`
Write the following function in the simplest form:
`tan^(-1) x/(sqrt(a^2 - x^2))`, |x| < a
Write the following function in the simplest form:
`tan^(-1) ((3a^2 x - x^3)/(a^3 - 3ax^2)), a > 0; (-a)/sqrt3 <= x a/sqrt3`
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 `tan^(-1) 1/5 + tan^(-1) (1/7) + tan^(-1) 1/3 + tan^(-1) 1/8 = pi/4`
Prove that:
`cot^(-1) ((sqrt(1+sin x) + sqrt(1-sinx))/(sqrt(1+sin x) - sqrt(1- sinx))) = x/2`, `x in (0, pi/4)`
sin (tan–1 x), | x| < 1 is equal to ______.
sin–1 (1 – x) – 2 sin–1 x = `pi/2` , then x is equal to ______.
Solve the following equation for x: `cos (tan^(-1) x) = sin (cot^(-1) 3/4)`
Prove that `3sin^(-1)x = sin^(-1) (3x - 4x^3)`, `x in [-1/2, 1/2]`
Prove that
\[2 \tan^{- 1} \left( \frac{1}{5} \right) + \sec^{- 1} \left( \frac{5\sqrt{2}}{7} \right) + 2 \tan^{- 1} \left( \frac{1}{8} \right) = \frac{\pi}{4}\] .
Find the value of `tan(sin^-1 3/5 + cot^-1 3/2)`
Prove that `tan^-1x + tan^-1y + tan^-1z = tan^-1[(x + y + z - xyz)/(1 - xy - yz - zx)]`
Solve: `2tan^-1 (cos x) = tan^-1 (2"cosec" x)`
Choose the correct alternative:
If `sin^-1x + sin^-1y = (2pi)/3` ; then `cos^-1x + cos^-1y` is equal to
Choose the correct alternative:
`sin^-1 3/5 - cos^-1 13/13 + sec^-1 5/3 - "cosec"^-1 13/12` is equal to
Evaluate `tan^-1(sin((-pi)/2))`.
Evaluate: `tan^-1 sqrt(3) - sec^-1(-2)`.
If y = `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))` for all x, then ______ < y < ______.
The value of cot–1(–x) for all x ∈ R in terms of cot–1x is ______.
If `"cot"^-1 (sqrt"cos" alpha) - "tan"^-1 (sqrt"cos" alpha) = "x",` the sinx is equal to ____________.
If `"tan"^-1 (("x" - 1)/("x" + 2)) + "tan"^-1 (("x" + 1)/("x" + 2)) = pi/4,` then x is equal to ____________.
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 Simplest form of `cot^-1 (1/sqrt(x^2 - 1))`, |x| > 1 is
What is the value of cos (sec–1x + cosec–1x), |x| ≥ 1
If sin–1x + sin–1y + sin–1z = π, show that `x^2 - y^2 - z^2 + 2yzsqrt(1 - x^2) = 0`
