Advertisements
Advertisements
Question
Simplify: `tan^-1 x/y - tan^-1 (x - y)/(x + y)`
Advertisements
Solution
`tan^-1 x/y - tan^-1 (x - y)/(x + y) = tan^-1 [(x/y - (x - y)/(x + y))/(1 + (x/y)((x - y)/(x + y)))]`
= `tan^-1 [((x(x + y) - y(x - y))/(y(x + y)))/(1 + (x(x - y))/(y(x + y)))]`
= `tan^-1 [(((x^2 + xy - xy + y^2))/(y(x + y)))/((y(x + y) + x(x - y))/(y(x + y)))]`
= `tan^-1 [(x^2 + y^2)/(xy + y^2 + x^2 - xy)]`
= `tan^-1 [(x^2 + y^2)/(x^2 + y^2)]`
= `tan^-1(1) = pi/4`
APPEARS IN
RELATED QUESTIONS
Prove that `cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=x/2;x in (0,pi/4) `
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 following function in the simplest form:
`tan^(-1) (sqrt((1-cos x)/(1 + cos x)))`, 0 < x < π
Find the value of the given expression.
`tan^(-1) (tan (3pi)/4)`
Find the value of the given expression.
`tan(sin^(-1) 3/5 + cot^(-1) 3/2)`
Prove that:
`tan^(-1) sqrtx = 1/2 cos^(-1) (1-x)/(1+x)`, x ∈ [0, 1]
Solve the following equation:
2 tan−1 (cos x) = tan−1 (2 cosec x)
If y = `(x sin^-1 x)/sqrt(1 -x^2)`, prove that: `(1 - x^2)dy/dx = x + y/x`
Find the value of `sin^-1[cos(sin^-1 (sqrt(3)/2))]`
If tan–1x + tan–1y + tan–1z = π, show that x + y + z = xyz
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
Evaluate tan (tan–1(– 4)).
If `"tan"^-1 ("cot" theta) = 2theta, "then" theta` is equal to ____________.
`"sin" {2 "cos"^-1 ((-3)/5)}` is equal to ____________.
The value of expression 2 `"sec"^-1 2 + "sin"^-1 (1/2)`
Find the value of `tan^-1 [2 cos (2 sin^-1 1/2)] + tan^-1 1`.
Write the following function in the simplest form:
`tan^-1 ((cos x - sin x)/(cos x + sin x)), (-pi)/4 < x < (3 pi)/4`
