TS EAMCET · Maths · Inverse Trigonometric Functions
Consider the following statements
Statement-I: \(\operatorname{Cosh}^{-1} x=\operatorname{Tanh}^{-1} x\) has no solution
Statement-II: \(\operatorname{Cosh}^{-1} x=\operatorname{Coth}^{-1} x\) has only one solution
The correct answer is
- A Both statements I and II are true
- B Both statements I and II are false
- C Statement I is true, but statement II is false
- D Statement I is false, but statement II is true
Answer & Solution
Correct Answer
(A) Both statements I and II are true
Step-by-step Solution
Detailed explanation
For Statement-I: \(\operatorname{Cosh}^{-1} x=\operatorname{Tanh}^{-1} x\) Domain of \(\operatorname{Cosh}^{-1} x\) is \([1, \infty)\). Domain of \(\operatorname{Tanh}^{-1} x\) is \((-1, 1)\). Intersection of domains is empty. Thus, no solution exists. Statement-I is true. For…
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