Question 1203876
next time don't copy and past, it is very hard to read what question is


Use trigonometric identities to transform the left side of the equation into the right side 

({{{0 < theta < pi/2}}})

proof that left side is equal to right side


{{{tan(theta)* cos(theta)  = sin(theta) }}}


Use trigonometric identity: {{{tan (theta) =sin(theta) /cos(theta)}}}


{{{(sin(theta) /cos(theta))*cos (theta)  = sin(theta) }}}


{{{(sin(theta) /cross(cos (theta))) cross(cos (theta))  = sin(theta) }}}


{{{sin(theta)  = sin(theta) }}}




Use trigonometric identities to transform the left side of the equation into the right side

({{{0 < theta < pi/2}}})
.

{{{cot(theta) sin(theta) =cos(theta)}}}

Use trigonometric identity: {{{cot(theta) = cos (theta)/sin(theta)}}}

{{{(cos (theta)/sin(theta))sin(theta) =cos (theta)}}}

{{{(cos (theta)/cross(sin(theta)))cross(sin(theta) )=cos (theta)}}}

{{{cos (theta)=cos (theta)}}}



Use trigonometric identities to transform the left side of the equation into the right side ({{{0 < theta < pi/2}}})



{{{(1 + cos (theta))( 1 - cos (theta) )=sin^2(theta)}}}
 {{{1 - cos^2 (theta) =sin^2(theta)}}}........use identity {{{sin^2(theta)+cos^2 (theta) =1}}}, then {{{sin^2(theta)=1 - cos^2 (theta) }}}

{{{sin^2(theta)=sin^2(theta)}}}




Use trigonometric identities to transform the left side of the equation into the right side  ({{{0 < theta < pi/2}}})


{{{sin^2(theta)-cos^2 (theta)=2sin^2(theta)-1}}}.....use identity {{{sin^2(theta)+cos^2 (theta) =1}}}, then {{{cos^2(theta)=1 - sin^2 (theta) }}}

{{{sin^2(theta)-(1 - sin^2 (theta) )=2sin^2(theta)-1}}}

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

{{{2sin^2(theta)-1=2sin^2(theta)-1}}}



Use trigonometric identities to transform the left side of the equation into the right side  ({{{0 < theta < pi/2}}})


{{{sin(theta)/cos(theta)+cos (theta)/sin(theta)=csc(theta) * sec (theta)}}}


use identities: {{{sin(theta)=1/csc(theta)}}} and {{{cos(theta)=1/sec(theta)}}}


{{{((1/csc(theta))/(1/sec(theta)))+(1/sec(theta))/(1/csc(theta) )=csc(theta) * sec(theta)}}}


{{{(sec(theta)/csc(theta))+(csc(theta)/sec(theta))=csc(theta) * sec (theta)}}}


{{{(sec^2(theta)+csc^2(theta))/(csc(theta) * sec (theta))=csc(theta) * sec (theta)}}}


use identity {{{sec^2(theta)+csc^2(theta)=csc^2(theta) sec^2(theta)}}}


{{{(csc^2(theta) sec^2(theta))/(csc(theta) * sec (theta))=csc(theta) * sec (theta)}}}...simplify


{{{csc(theta) *sec (theta)=csc(theta) * sec (theta)}}}