Verified answer

Answer:

Prove that [sin theata/1+cos theata] + [(1+cos theata)/sin theata] = 2Cosec theata

Step-by-step explanation:

Consider LHS, taking LCM

sin2theata + (1+cos2theata)2/sin theata (1+cos theata)

= [sin2theata + 1 + 2cos theata + cos2 theata] /sin theata(1+cos theata)

= (sin2theata  + cos2theata + 1 + 2cos theata )/sin theata(1+cos theata)

= (1+1+2cos theata)/sin theata(1+cos theata)

= (2 + 2cos theata)/sin theata (1+costheata)

= 2(1 + cos theata)/sin theata(1+cos theata)

= 2/sin theata (Cancelling 1+cos theata term from Nr and Dr)

= 2Cosec theata

Hence proved.

Answer:

Consider LHS, taking LCM sin2theata + (1+cos2theata)2/sin theata (1+cos theata)

= [sin2theata + 1+ 2cos theata + cos2 theata] /sin theata(1+cos theata)

= (sin2theata + cos2theata + 1 + 2cos

theata )/sin theata(1+cos theata)

= (1+1+2cos theata)/sin theata(1+cos

theata)

= (2+2cos theata)/sin theata (1+costheata)

= 2(1 + cos theata)/sin theata(1+cos

theata)

= 2/sin theata (Cancelling 1+cos theata term from Nr and Dr)

= 2Cosec theata

Hence proved.

Step-by-step explanation:

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