Trigonometry

We assume the following is the correct expression to be simplified.

[(1+sin2A)  +  (1-sin2A)] / [(1+sin2A) - (1-sin2A)]

Simplify using the following trignometric identities,

sin² A + cos² A = 1 and sin2A = 2sinAcosA

(1+sin2A) = (sin² A + cos² A + 2sinAcosA) = (sin A + cos A)² = (sin A + cos A)

(1-sin2A) = (sin² A + cos² A - 2sinAcosA) = (sin A - cos A)² = (sin A - cos A)

[(1+sin2A)  +  (1-sin2A)] / [(1+sin2A) - (1-sin2A)] =

 [(sin A + cos A) + (sin A - cos A)] / [(sin A + cos A) - (sin A - cos A)] =

= tan A

Regards,

Team,

TopperLearning.