Prove that (sin θ) (cos θ) = tan θ/( 1 + tan^2 θ )

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Prove that (sin θ) (cos θ) = tan θ/( 1 + tan ^{2} θ )

This is a question from class 10 maths ICSE book (Understanding ICSE mathematics). This chapter is Trigonometric Identities from ML Aggarwal(SELINA Publishers).

RHS = tan θ/ sec

^{2}θ= (sin θ/ cos θ )/ sec

^{2}θ=(sin θ X cos

^{2}θ)/ cos θsin θ X cos θ