Project ForgeEngineering Mathematics
Complex Variables
GATE 2020
Easy
Match the hyperbolic functions in Group-1 with their definitions in Group-2. Group-1: P-tanh x, Q-coth x, R-sech x, S-cosech x. Group-2: I-(eˣ+e⁻ˣ)/(eˣ−e⁻ˣ), II-2/(eˣ+e⁻ˣ), III-2/(eˣ−e⁻ˣ), IV-(eˣ−e⁻ˣ)/(eˣ+e⁻ˣ). The correct combination is
- AP–IV, Q–I, R–III, S–II
- BP–II, Q–III, R–I, S–IV
- P–IV, Q–I, R–II, S–III
- DP–I, Q–II, R–IV, S–III
Explanation
tanh x=(eˣ−e⁻ˣ)/(eˣ+e⁻ˣ)=IV. coth x=(eˣ+e⁻ˣ)/(eˣ−e⁻ˣ)=I. sech x=2/(eˣ+e⁻ˣ)=II. cosech x=2/(eˣ−e⁻ˣ)=III. So P–IV, Q–I, R–II, S–III.
Source: GATE CH 2020 (2020)
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