Question

Prove that ( sin theata + 1 + cos theata ) ( sin theata - 1 + cos theata ) . Sec theata cosec theata =2

Answer 1

Answer:

Step-by-step explanation:

(Sinθ + 1 + Cosθ)(Sinθ - 1 + Cosθ)Secθ*Cosecθ

= (Sinθ + Cosθ + 1) (Sinθ + Cosθ - 1)Secθ*Cosecθ

=  [(Sinθ + Cosθ)² - (1)²]Secθ*Cosecθ

=  [(Sinθ + Cosθ)² - 1]Secθ*Cosecθ

= [Sin²θ+ Cos²θ+2SinθCosθ - 1]Secθ*Cosecθ

= [1 + 2SinθCosθ - 1]Secθ*Cosecθ

= (2SinθCosθ)Secθ*Cosecθ

= 2SinθCosθ / SinθCosθ

= 2

= R.H.S