Q24 of 76 Page 52

If x = sec ϕ – tan ϕ and y = cosec ϕ + cot ϕ, then show that xy + x – y + 1 = 0.

[Hint: Find xy + 1 and then show tan x – y = –(xy + 1)]

Given,


x = sec ϕ – tan ϕ and y = cosec ϕ + cot ϕ


To prove: xy + x – y + 1 = 0


∵ LHS = xy + x – y + 1









{∵ sin2θ + cos2θ = 1}


Thus, LHS = xy + x – y + 1 = 0


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