If `P(x) =[(cos x, -sin x),(sin x , cos x)]`, then show that `P(A) P(B)=P(A+B)`.

If A={a,b},B={b,c} Find P(A), P(B), P(A) uu P(B) , P(A) nn P(B) show that P(A) nn P(B) = P(A nn B)

If y=x^(sin x) + (sinx)^(cos x) ,then find (dy)/(dx) .

If x=r cos0 and y=r sin0 , then show that (d y)/(dx)+(x)/(y)=0 .

Simplify tan^(-1) [(a cos x -b sin x)/(b cos x +a sin x)] , if (a)/(b) tan x gt -1 .

If A={a,b},B={b,c} Find P(A), P(B), P(A) uu P(B) , P(A) nn P(B) show that P(A) uu P(B) sub P(A uu B)

If 3 sin x + 5 cos x = 5, show that 3 cos x - 5 sin x = +- 3 .

Prove that f(x) = sin x and f(x) = cos x are continuous.

Integrate the function int (4 cos x-3 sin x)/((8 sin x + 6 cos x)^(2))dx.

x and y are two positive integers such that 2,x, y are in A.P. and x, y, 9 are in G.P. then show that -x= 4, y= 6.