Statements S and R are as follows:

S : sin x and cosx both are decreasing functions in ,
2
  
    
R : if a differentiable function is decreasing in a,b then its derivative is also decreasing in a,b
Which of the following statements is correct?
(1) Both S and R are false
(2) Both S and R are true but R is not correct explanation of S
(3) S is true and R is correct explanation of S
(4) S is true but R is false

1 answer

The correct answer is (3) S is true and R is correct explanation of S.

S states that sin(x) and cos(x) are both decreasing functions in the interval [0,π/2]. This is true because in this interval, both sin(x) and cos(x) start at their maximum value (1) and decrease as x increases.

R states that if a differentiable function is decreasing in an interval (a,b), then its derivative is also decreasing in that interval. This is true because if a function is decreasing, its derivative will be negative, indicating a decrease in the rate of change.

Therefore, S is true and R is a correct explanation of S.