# Answer to Question #21700 in Trigonometry for Meredith

Question #21700

how do you simplify tan(theta) sin(theta) sec(theta)?

Expert's answer

We know that

tan(theta)=sin(theta)/cos(theta)

sec(theta)=1/cos(theta)So we have tan(theta) sin(theta) sec(theta)=[sin(theta)/cos(theta) ] * sin (theta) * [ 1/cos(theta) ]=sin^2 (theta) /

cos^2(theta)= =[ sin(theta)/cos(theta)]^2=[tan(theta)]^2

tan(theta)=sin(theta)/cos(theta)

sec(theta)=1/cos(theta)So we have tan(theta) sin(theta) sec(theta)=[sin(theta)/cos(theta) ] * sin (theta) * [ 1/cos(theta) ]=sin^2 (theta) /

cos^2(theta)= =[ sin(theta)/cos(theta)]^2=[tan(theta)]^2

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