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Consider the following statments in S and R
S : Both sin x and cos x are decreasing functions in the 
R: If a differentiable function decreases in an interval (a, b), then its derivative also decreases in (a, b).
Which of the following is true ?
  • a)
    Both S and R are wrong
  • b)
    Both S and R are correct, but R is not the correct explanation of S
  • c)
    S is correct and R is the correct explanation for S
  • d)
    S is correct and R is wrong
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Consider the following statments in S and RS : Both sin x and cos x ar...
From graph it is clear that both sin x and cos x in the interval (π / 2,π) are decreasing function.
∴ S is correct.
To disprove R let us consider the counter example :
f (x) = sin x on (0, π / 2) so that f '(x) = cosx
Again from graph it is clear that f (x) is increasing on (0, π / 2) but f '(x) is decreasing on (0, π / 2)
∴ R is wrong.
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Consider the following statments in S and RS : Both sin x and cos x ar...
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Consider the following statments in S and RS : Both sin x and cos x ar...
From graph it is clear that both sin x and cos x in the interval (π / 2,π) are decreasing function.
∴ S is correct.
To disprove R let us consider the counter example :
f (x) = sin x on (0, π / 2) so that f '(x) = cosx
Again from graph it is clear that f (x) is increasing on (0, π / 2) but f '(x) is decreasing on (0, π / 2)
∴ R is wrong.
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Consider the following statments in S and RS : Both sin x and cos x are decreasing functions in theR: If a differentiable function decreases in an interval (a, b), then its derivative also decreases in (a, b).Which of the following is true ?a)Both S and R are wrongb)Both S and R are correct, but R is not the correct explanation of Sc)S is correct and R is the correct explanation for Sd)S is correct and R is wrongCorrect answer is option 'D'. Can you explain this answer?
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Consider the following statments in S and RS : Both sin x and cos x are decreasing functions in theR: If a differentiable function decreases in an interval (a, b), then its derivative also decreases in (a, b).Which of the following is true ?a)Both S and R are wrongb)Both S and R are correct, but R is not the correct explanation of Sc)S is correct and R is the correct explanation for Sd)S is correct and R is wrongCorrect answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Consider the following statments in S and RS : Both sin x and cos x are decreasing functions in theR: If a differentiable function decreases in an interval (a, b), then its derivative also decreases in (a, b).Which of the following is true ?a)Both S and R are wrongb)Both S and R are correct, but R is not the correct explanation of Sc)S is correct and R is the correct explanation for Sd)S is correct and R is wrongCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statments in S and RS : Both sin x and cos x are decreasing functions in theR: If a differentiable function decreases in an interval (a, b), then its derivative also decreases in (a, b).Which of the following is true ?a)Both S and R are wrongb)Both S and R are correct, but R is not the correct explanation of Sc)S is correct and R is the correct explanation for Sd)S is correct and R is wrongCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Consider the following statments in S and RS : Both sin x and cos x are decreasing functions in theR: If a differentiable function decreases in an interval (a, b), then its derivative also decreases in (a, b).Which of the following is true ?a)Both S and R are wrongb)Both S and R are correct, but R is not the correct explanation of Sc)S is correct and R is the correct explanation for Sd)S is correct and R is wrongCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
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