Consider the following statements in S and R S: Both `sinxa n dcosx` are decrerasing function in the interval `(pi/2,pi)` R: If a differentiable function decreases in an interval `(a , b),` then its derivative also decrease in `a , b)dot` Which of the following it true? Both S and R are wrong. Both S and R are correct, but R is not the correct explanation of S. S is correct and R is the correct explanation for S. S is correct and R is wrong.

Options

A. Both S and R are wrong
B. Both S and R are correct , but R is not the correct explanation ofS.
C. S is correct and R is the correct explanation for S.
D. S is correct and R is wrong.

Answer

4

Explanation

Form the graph it is clear that both sinxand cos x in the internal `(pi//2,pi)` are the decreasing functions.

Therefore S is correct.
To disprove R, let us consider the counter example
`f(X)=sinx in (0,pi//2)`
So that f(X) = cos x
Again from the graph it is clear that f(X) is increasing in `(0,pi//2)`
Therefore R is wrong .Therefore (4) is the correct option