Advertisements
Advertisements
प्रश्न
Find the value, if it exists. If not, give the reason for non-existence
`sin^-1 (cos pi)`
Advertisements
उत्तर
`sin^-1 (cos pi) = sin^-1(- 1)`
= `- sin^-1 (1)`
= `- pi/2` ......[∵ cos π = – 1]
APPEARS IN
संबंधित प्रश्न
Prove that: `tan^(-1)(1/2)+tan^(-1)(1/5)+tan^(-1)(1/8)=pi/4`
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 [sin^(-1) (2x)/(1+ x^2) + cos^(-1) (1-y^2)/(1+y^2)]`, |x| < 1, y > 0 and xy < 1
Solve for x : \[\tan^{- 1} \left( \frac{x - 2}{x - 1} \right) + \tan^{- 1} \left( \frac{x + 2}{x + 1} \right) = \frac{\pi}{4}\] .
Solve for x : \[\cos \left( \tan^{- 1} x \right) = \sin \left( \cot^{- 1} \frac{3}{4} \right)\] .
Solve: `tan^-1x = cos^-1 (1 - "a"^2)/(1 + "a"^2) - cos^-1 (1 - "b"^2)/(1 + "b"^2), "a" > 0, "b" > 0`
Choose the correct alternative:
sin(tan–1x), |x| < 1 is equal to
If α ≤ 2 sin–1x + cos–1x ≤ β, then ______.
Solve for x : `"sin"^-1 2 "x" + sin^-1 3"x" = pi/3`
`"sin" {2 "cos"^-1 ((-3)/5)}` is equal to ____________.
`"tan"^-1 1/3 + "tan"^-1 1/5 + "tan"^-1 1/7 = "tan"^-1 1/8 =` ____________.
Simplest form of `tan^-1 ((sqrt(1 + cos "x") + sqrt(1 - cos "x"))/(sqrt(1 + cos "x") - sqrt(1 - cos "x")))`, `π < "x" < (3π)/2` is:
`"cos" (2 "tan"^-1 1/7) - "sin" (4 "sin"^-1 1/3) =` ____________.
`"sin"^-1 (1/sqrt2)`
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 ∠CAB = ________.
The Simplest form of `cot^-1 (1/sqrt(x^2 - 1))`, |x| > 1 is
Find the value of `sin^-1 [sin((13π)/7)]`
If `cos^-1(2/(3x)) + cos^-1(3/(4x)) = π/2(x > 3/4)`, then x is equal to ______.
