Question

Show that
`(cos^(2)theta - sin^(2)theta)=(2tan theta)/((1- tan^(2)theta)) ` is not an identity .

Answer 1

Putting ` theta = 30^(@), ` we find :
` LHS = (cos^(2)30^(@)- sin^(2)30^(@)) `
`={((sqrt(3))/(2))^(2)-((1)/(2))^(2)}=((3)/(4) - (1)/(4)) = (2)/(4)=(1)/(2), and `
` RHS = (2 tan 30^(@))/((1- tan^(2)30^(@)))=(2 xx (1)/(sqrt(3)))/([1-((1)/(sqrt(3)))^(2)])=((2)/(sqrt(3)))/((1- (1)/(3)))=((2)/(sqrt(3)) xx (3)/(2)) = sqrt(3). `
` therefore LHS ne RHS. `
Hence, the given equation is not an identity.