Maths · Trigonometrical identities and trigonometrical functions
Assertion The equation has infinite number of solutions Reason The domain of =\s
Assertion The equation \( \sin x=1, \) has infinite number of solutions Reason The domain of \( f(x)=\sin x \) is \( (-\infty, \infty) \)
- A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
- B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
- C. Assertion is correct but Reason is incorrect
- D. Assertion is incorrect but Reason is correct
Step-by-step solution
Assertion: sin x = 1 has solutions x = π/2 + 2kπ for integer k, which are infinite due to the periodic nature of sine. Reason: The domain of sin x is all real numbers, which is true but does not explain the infinite solutions; the periodicity is the key. Thus both are correct but reason is not the correct explanation.
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