1.

62, Prove that: (1 + cot A-cosec A)(1 + tan A +sec A) 2.CRSE 200

Answer»

L.H.S = ( 1+ cota-coseca) ( 1+ tana -seca)

= (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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