Question 864368
Sin theta + Cos theta + (Tan theta)(Sin theta) = Sec theta + (Cos theta)(Tan theta)

LHS
{{{Sin (theta) + Cos (theta) + (Tan (theta))(Sin (theta))}}}

{{{Sin (theta) + Cos (theta) + (sin (theta)/cos(theta))(Sin (theta))}}}



{{{(Sin (theta)*cos(theta) + Cos^2 (theta) + sin^2 (theta))/cos(theta)}}}


{{{(Sin (theta)*cos(theta))/cos(theta) + (1/cos(theta))}}}

{{{sin (theta)+1/cos(theta)}}}

={{{sin (theta) +sec(theta)}}}

Simplify RHS


Sec theta + (Cos theta)(Tan theta)

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

={{{sin (theta) +sec(theta)}}}


LHS = RHS