If y=a sinx +b cosx, prove that y^2+dy/dx^2=a^2+b^2
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Step-by-step explanation:
y =a sin x + b cos x , let A =[a^2 +b^2]^(1/2)
then sin e= a/A , cos e = b/A
y = A[a/A sin x + b/A cos x]
y =A[ sin e . sin x + cos e . cos x]
y = A [ cos( x-e)]
y is a maximum when cos [x-e] is max . ,that is cos[x-e]=1
[x-e ] = arc cos [1] = 2n pi ,then
max y = A = [a^2 +b^2]^(1/2)
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