Mathematics Tes...

If tan^-1 2, tan^-1 3 are two angles of a triangle, then what is the third angle?

Evaluate:

\(2(\sec A-\cos A)^{2}+2(\operatorname{cosec} A-\sin A)^{2}-2(\cot A-\tan A)^{2}-2\)

What is the sum of the squares of direction cosines of X-axis?

Find the standard deviation of \(\{7,13,15,11,4\}\).

Find the probability that in a random arrangement of the letters of the word 'UNIVERSITY' the two I's do not come together?

Two cards are drawn at random and without replacement from a pack of \(52\) playing cards. Find the probability that both the cards are black:

If \(y=\tan ^{-1}\left[\frac{3 a^{2} x-x^{3}}{a\left(a^{2}-3 x^{2}\right)}\right],\) then find out \(\frac{d y}{d x}\)

Find the value of \(\frac{(\sin x+\cos x+1)(\sin x+\cos x-1)}{(\tan x+\cot x)\left(\sin ^{2} x \cos ^{2} x\right)}\):

A dice is tossed thrice. Find the probability of getting an odd number at least once: