Question 1188496


prove 

{{{tan^2(theta)sin^2(theta)=tan^2(theta)+cos^2(theta)-1}}}

manipulate left side

{{{tan^2(theta)sin^2(theta)}}}...........use identity {{{sin^2(theta)=1-cos^2(theta)}}}

={{{tan^2(theta)(1-cos^2(theta))}}}

={{{tan^2(theta)-tan^2(theta)cos^2(theta)}}}........use identity {{{tan^2(theta)=sin^2(theta)/cos^2(theta)}}}

={{{tan^2(theta)-(sin^2(theta)/cos^2(theta))cos^2(theta)}}}

={{{tan^2(theta)-sin^2(theta)}}} ........use identity  {{{sin^2(theta)=1-cos^2(theta)}}}

={{{tan^2(theta)- (1-cos^2(theta))}}}

={{{tan^2(theta)- 1+cos^2(theta)}}}

={{{tan^2(theta)+cos^2(theta)-1}}}