| Assertion [A]: The intervals is which \[f\left( x \right)\text{ }=\text{ }log\text{ }sinx\], \[0\le \text{ }x\text{ }\le \pi \] is increasing is \[\left( 0,\frac{\pi }{2} \right)\]. |
| Reason [R]: The function tan x is + ve in first quadrant |
A) Both A and R are individually true and R is the correct explanation of A.
B) Both A and R are individually true and R is not the correct explanation of A.
C) 'A' is true but 'R' is false
D) 'A' is false but 'R' is true
E) Both A and R are false.
Correct Answer: A
Solution :
Given, \[f\,(x)=log\,\,sin\,x\,\Rightarrow f'(x)=\frac{1}{\sin x}.\cos x=\cot x\] For increasing function,\[~f'\left( x \right)>0\Rightarrow cot\text{ }x>0\] \[\therefore \] Assertion [A] is true. We know that tan x is +ve in first quadrant \[\therefore \text{ }cot\text{ }x\] is \[+\,ve\] \[\therefore \] Reason R is true and is correct explanation of A Hence option [A] is the correct answer.
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