Advertisements
Advertisements
Question
Find the value of `cot[sin^-1 3/5 + sin^-1 4/5]`
Advertisements
Solution
`cot[sin^-1 3/5 + sin^-1 4/5]`
= `cot [sin^-1 (3/5 sqrt(1 - (4/5)^2) + 4/5 sqrt(1 - (3/5)^2))]`
= `cot[sin^-1 (3/5 sqrt(1 - 16/25) + 4/5 sqrt(1 - 9/25))]`
= `cot [sin^-1 (3/5 sqrt(9/25) + 4/5 sqrt(16/25))]`
= `cot [sin^-1 (3/5 xx 3/5 + 4/5 xx 4/5)]`
= `cot[sin^-1 (9/25 + 16/25)]`
= `cot[sin^-1 (25/25)]`
= `cot [sin^-1(1)]`
= `cot pi/2`
= 0
APPEARS IN
RELATED QUESTIONS
If a line makes angles 90°, 60° and θ with x, y and z-axis respectively, where θ is acute, then find θ.
Find the value of the given expression.
`sin^(-1) (sin (2pi)/3)`
Find the value of the given expression.
`tan(sin^(-1) 3/5 + cot^(-1) 3/2)`
sin–1 (1 – x) – 2 sin–1 x = `pi/2`, then x is equal to ______.
Prove that `3sin^(-1)x = sin^(-1) (3x - 4x^3)`, `x in [-1/2, 1/2]`
Choose the correct alternative:
`sin^-1 3/5 - cos^-1 13/13 + sec^-1 5/3 - "cosec"^-1 13/12` is equal to
Choose the correct alternative:
The equation tan–1x – cot–1x = `tan^-1 (1/sqrt(3))` has
Choose the correct alternative:
sin(tan–1x), |x| < 1 is equal to
Evaluate `tan^-1(sin((-pi)/2))`.
Solve the equation `sin^-1 6x + sin^-1 6sqrt(3)x = - pi/2`
The value of the expression tan `(1/2 "cos"^-1 2/sqrt3)`
If sin `("sin"^-1 1/5 + "cos"^-1 "x") = 1,` then the value of x is ____________.
sin (tan−1 x), where |x| < 1, is equal to:
The value of `"tan"^-1 (3/4) + "tan"^-1 (1/7)` is ____________.
`"sin"^-1 (1 - "x") - 2 "sin"^-1 "x" = pi/2`
`"sin"^-1 ((-1)/2)`
Find the value of `sin^-1 [sin((13π)/7)]`
`tan^-1 sqrt3 - cot^-1 (- sqrt3)` is equal to ______.
If \[\tan^{-1}\left(\frac{x}{2}\right)+\tan^{-1}\left(\frac{y}{2}\right)+\tan^{-1}\left(\frac{z}{2}\right)=\frac{\pi}{2}\] then xy + yz + zx =
