how to simplify

Question

[sin(180°−a)×tan (180°+a)×cos (360°−a) ] ÷ [ tan (360°−a)×cos (180°−a) ]

Answer 1

The expression is [sin(180° - a)tan(180° + a)cos(360 - a)] / [ tan(360° - a)cos(180 - a)]

Recall the circular function formulae

sin(180° - x) = sinx

tan(180° + x) = tanx

cos(360 - x) = cosx

tan(360° - a) = - tanx

cos(180 - a) = - cosx

[sin(180° - a)tan(180° + a)cos(360 - a)] / [ tan(360° - a)cos(180 - a)]

= [sina tana cosa ]/ [ (- tana )(-cosa)

= [ sina (sina/cosa) cosa ] / [ tana cosa]

= [sin² a]/[ (sina/cosa)cosa]

= sin² a / sina

= sina