Solve for x, given \( \tan^{-1}\left(\frac{1 - x}{1 + x}\right) = \frac{1}{2} \tan^{-1}(x) \)
If x2 + 2px - 2p + 8 > 0 for all real values of x, then the set of all possible values of p is
If \(1+ (√1+x) tanx = 1+ (√1-x)\) then \(sin4x\) is ?
If x dy= y(dx + ydy), x(1)=1, y(x)>0, then y (-3) is?
The principal value of sin-1(sin 3ℼ/4) is?
Solution of sinx + sin5x = sin 3x in (0,ℼ/2) are..?
Solution of \( (1 + xy) \, y \, dx + (1 - xy) \, x \, dy = 0 \) is?
Variance of first 2n natural numbers?
Rolle Theorem f(x) = sin x + cos x. Find c ε [0,2,π]
Differentiate \(tan^{-1}(\frac{\sqrt{1+x^2}-1}{x}) \,w.r.t\,\,cos^{-1}(\frac{\sqrt(1+\sqrt{1+x^2})}{2\sqrt({i}+x^2)})\)
Mean + Variance = 1.8, n = 5, Find p(probability of success).
Find variance of first 2n natural numbers.
\( \sum (x - x_i)^2 = 100 \), no. of observations = 20, \( \sum x_i = 20 \).
Find cos248o - sin212o , if sin18o = (√5 - 1)/4
If a pair of line given by \( (x \cos \alpha + y \sin \alpha)^2 = (x^2 + y^2) \sin^2 \alpha \) are perpendicular. What is the value of α?
\( \lim_{x \to 0} \frac{x \cdot \cot(4x)}{\sin(2x) \cdot \cot^2(2x)} = ? \)