`Assertion` Consider the following statements in `S and R S:` Both `sinx and cosx` are decrerasing function in the interval `(pi/2,pi) ` `Reason` If a differentiable function decreases in an interval `(a,b)`, then its derivative also decrease in `(a,b)`.Which of the following it 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.

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