Q2 of 104 Page 204

Prove the following by using trigonometric identities:

2sin2θ + 4sec2θ + 5cot2θ + 2cos2θ — 4tan2θ — 5cosec2θ = 1

L.H.S

2sin2θ + 4sec2θ + 5cot2θ + 2cos2θ — 4tan2θ — 5cosec2θ


= (2sin2θ + 2cos2θ) + ( 4sec2θ – 4tan2) + (5cot2θ — 5cosec2θ)


= 2 + 4 – 5


= 1


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