If `x^n=a^m cos^4 theta ` and `y^n = b^m sin^4 theta` then `(i) (x^(n/2))/(a^(m/2))+ (y^(n/2))/(b^(m/2))=1` `(ii) x^n/a^m+y^n/b^m=1`(iii) `(x^(n/2))/(y^(n/2))+ (a^(m/2))/(y^(m/2))=1` (iv) None of these

If a cos theta+b sin theta=m and a sin theta-b cos theta=n, Prove that a^(2)+b^(2)=m^(2)+n^(2)

If a cos theta+b sin theta=m and a sin theta-b cos theta=n, prove that a^(2)+b^(2)=m^(2)+n^(2)

If a cos theta+b sin theta=m and a sin theta-b cos theta=n, then a^(2)+b^(2)=m^(2)-n^(2)(b)m^(2)n^(2)(c)n^(2)-m^(2)(d)m^(2)+n^(2)

If x^(m)y^(n)=(x+y)^(m+n), prove that (d^(2)y)/(dx^(2))=0

If x^(m)y^(n)=(x+y)^(m+n), prove that (d^(2)y)/(dx^(2))=0

If x^(m)y^(n)=(x+y)^(m+n), prove that (d^(2)y)/(dx^(2))=0

If x^(m)y^(n)=(x+y)^(m+n) , prove that : (d^(2)y)/(dx^(2))=0 .

Find the square root of (m^(n^(2))n^(m^(2))a^((m+n)))/((m+n)^((m+n)^(2) (i) (m^n)(n^m)a^((m+n)/2) (ii) ((m^(n^2))(n^(m^2))a^((m+n)/2))/(m+n)^(((m+n)^2)/2) (iii) (m^n)(n^m)a^(sqrt(m+n))/(m+n)^(((m+n))) (iv)none of these

If 2 cos alpha = x + (1)/(x) and 2 cos beta = y + (1)/(y) , show that (x^(m))/(y^(n))- (y^(n))/(x^(m))= 2i sin (m alpha - n beta)

If x and y are positive real numbers and m,n are any positive integers,then (x^(n)y^(m))/((1+x^(2n))(1+y^(2m)))<(1)/(4)