Asked by PRINCE
Prove that:1+tan^2x/tan^2x =Csc^2x
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GPT-5 mini
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Start with the left-hand side:
(1 + tan^2 x)/tan^2 x = 1/tan^2 x + 1 = cot^2 x + 1.
Use the Pythagorean identity for cotangent and cosecant:
1 + cot^2 x = csc^2 x.
Therefore (1 + tan^2 x)/tan^2 x = csc^2 x, for all x with tan x defined and nonzero (equivalently sin x ≠ 0).
(1 + tan^2 x)/tan^2 x = 1/tan^2 x + 1 = cot^2 x + 1.
Use the Pythagorean identity for cotangent and cosecant:
1 + cot^2 x = csc^2 x.
Therefore (1 + tan^2 x)/tan^2 x = csc^2 x, for all x with tan x defined and nonzero (equivalently sin x ≠ 0).
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