Prove that 1 cota coseca 1 tana seca 2
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Prove that ( 1+ cota-coseca) ( 1+ tana -seca) =2
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Answer:
L.H.S = ( 1+ cota-coseca) ( 1+ tana -seca)
Step-by-step explanation:
= (1+cosa/sina-1/sina) (1+sina/cosa-1/cosa)
= (sina+cosa-1/sina) (cosa+sina-1/cosa)
= ((sina+cosa) - (1)/sina) ((cosa+sina) - (1)/cosa)
= ((sina+cosa)raise to power2 - (1)raise to power 2)/sinacosa
= sin2a+cos2a+2sinacosa-1/sinacosa
= 1+2sinacosa-1/sinacosa (because sin2a+cos2a=1)
= 2sinacosa/sinacosa
=2
=R.H.S
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