Q28 of 58 Page 8


Prove that (sin θ + sec θ) 2+ (cos θ + cosec θ) 2=(1 + sec θ cosec θ) 2.


L.H.S = (sin θ + sec θ ) 2 + (cos θ + cosec θ ) 2
= [sin θ +(1/cos θ)] 2 + [cos θ + (1/sin θ) ] 2

= 1 + sec 2 θ cosec 2 θ + 2 sec θ cosec θ

= (1 + sec θ cosec θ) 2
= R.H.S.

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