If `theta=3alpha`and `sintheta=a/(sqrt(a^2+b^2)),` the value of the expression `acos e calpha-bsecalpha` is (a)`a/(sqrt(a^2+b^2))` (b) `2sqrt(a^2+b^2)` (c) `a+b` (d) none of these

If sintheta=a/(sqrt(a^(2)+b^(2))) , then show that bsintheta=acostheta .

If sintheta=(a)/(sqrt(a^(2)+b^(2))) then show that b sin theta = a cos theta .

IfI=int(dx)/((a^2-b^2x^2)^(3/2)),t h e nIe q u a l (a) x/(a^2sqrt(a^2-b^2x^2))+C (b) x/(2sqrt(a^2-b^2x^2))+C (c) (a x)/(sqrt(a^2-b^2x^2))+C (d) none of these

If a<0,b>0, then sqrt(a)sqrt(b) is equal to (a) -sqrt(|a|b) (b) sqrt(|a|b)i (c) sqrt(|a|b) (d) none of these

If asinx+bcos(x+theta)+bcos(x-theta)=d , then the minimum value of |costheta| is equal to (a) 1/(2|b|)sqrt(d^2-a^2) (b) 1/(2|a|)sqrt(d^2-a^2) (c) 1/(2|d|)sqrt(d^2-a^2) (d) none of these

If sintheta=a/(sqrt((a^(2)+b^(2)+c^(2)+2bc))) , then show that (b+c)sintheta=(a)costheta .

lim_(xto0)(sqrt(x^(2)+a^(2))-a)/(sqrt(x^(2)+b^(2))-b)

The solution for x of the equation int_(sqrt(2))^x(dt)/(tsqrt(t^2-1))=pi/2 is pi (b) (sqrt(3))/2 (c) 2sqrt(2) (d) none of these

If a ** b = sqrt(a^(2) + b^(2)) on the real numbers then ** is