Show that the straight line `x cosalpha+y sin alpha=p` is a tangent to the curve `(x^(m))/(a^(m))+(y^(m))/(b^(m))=1`, if
`(a cos alpha)^((m)/(m-1))+(b sin alpha)^((m)/(m-1))=p^((m)/(m-1))`

Find the condition that the line x cos alpha+y sin alpha=p may touch the curve ((x)/(a))^(m)+((y)/(b))^(m)=1

Find the condition that the line x cos alpha+y sin alpha=p may touch the curve ((x)/(a))^(m)+((y)/(b))^(m)=1

if the straight line x cos alpha+y sin alpha=p touches the curve x^(m)y^(n)=a^(m+n) prove that p^(m+n)m^(m)n^(n)=(m+n)^(m+n)a^(m+n)sin^(n)alpha cos^(m)alpha

If the straigjht line x cos alpha+ y sin alpha=p touches the curve x^(m)y^(n)=a^(m+n) , prove that. p^(m+n)""m^(m)n^(n)=(m+n)^(m+n)a^(m+n)sin^(n) alpha cos^(m) alpha

If the straight line x cosalpha+y sinalpha=p touches the curve x^my^n =a^(m+n) , prove that p^(m+n).m^m.n^n =(m+n)^(m+n)a^(m+n)cos^m alphasin^nalpha

If the line x cos alpha+y sin alpha= p touches the curve x^my^n= a^(m+n) prove that p^(m+n).m^m.n^n= a^(m+n)(m+n)^(m+n).cos^m alpha. Sin^n alpha .

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 = cos alpha + i sin alpha , y = cos beta + i sin beta , prove that x^(m)y^(n)+1/(x^m y^n) = 2 cos (m alpha + n beta) .

If m, n integers and x = cos alpha + i sin alpha , y = cos beta + i sin beta, then prove that x^(m) y^(n) + 1/(x^(m)y^(n)) = 2 cos ( m alpha + n beta) " and " x^(m) y^(n) - 1/(x^(m) y^(n)) = 2 i sin ( m alpha + n beta) .

If "tan" alpha= n tan beta and sin alpha =m sin beta prove that : cos^(2)alpha=(m^(2)-1)/(n^(2)-1)