1.

Prove the following : (sinθ + cosecθ)2 + (cos θ + see θ)2 = tan2 θ + cot2 θ + 7

Answer»

L.H.S. = (sinθ + cosecθ)2 + (cos θ + see θ)2 

= sin2 θ + cosec2 θ + 2sinθ cosec θ + cos2 θ + sec2 θ + 2sec0 cos0 

= (sin2 θ + cos2 θ) + cosec2 θ + 2 + sec2 θ + 2 

= 1 + (1 + cot2 θ) + 2 + (1 + tan2 θ) + 2 = tan2 θ + cot2 θ + 7 

= R.H.S



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