GATE 2020 CH – Question 12

Engineering Mathematics · Calculus: Limits, continuity, differentiability, Taylor series and mean value theorem · 1 mark · Multiple choice

Match P: tanh x, Q: coth x, R: sech x, S: cosech x with I: $(e^x+e^{-x})/(e^x-e^{-x})$; II: $2/(e^x+e^{-x})$; III: $2/(e^x-e^{-x})$; IV: $(e^x-e^{-x})/(e^x+e^{-x})$.

P–IV, Q–I, R–III, S–II
P–II, Q–III, R–I, S–IV
P–IV, Q–I, R–II, S–III
P–I, Q–II, R–IV, S–III

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Show answer and explanation

Correct answer: (C) P–IV, Q–I, R–II, S–III

Explanation

Use $\sinh x=(e^x-e^{-x})/2$ and $\cosh x=(e^x+e^{-x})/2$. Their ratio gives tanh → IV and the reciprocal gives coth → I. Reciprocals of cosh and sinh give sech → II and cosech → III. The matching choice is C, on each function’s domain.

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