1.

Prove that [1 + cot α - sec(α + (π/2))][1 + cot α + sec(α + (π/2))] = 2cot α

Answer»

sec(α + π/2) = - cosec α

LHS = [(1 + cot α) + cosec α][(1 + cot α) – cosec α] 

= (1 + cot α)2 – cosec2 α 

= 1 + cot2 α + 2 cot α – cosec2 α 

[∵ 1 + cot2 α = cosec2 α]

= cosec2 α + 2 cot α – cosec2 α 

= 2 cot α = RHS



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