Question -
Answer -
Given f (x) = cos2┬аx
тЗТ┬а
тЗТ┬аfтАЩ(x)= 2 cos x (тАУsin x)
тЗТ┬аfтАЩ(x)= тАУ2 sin (x) cos (x)
тЗТ┬аfтАЩ(x)= тАУsin2x
Now, as given x belongs to (0, ╧А/2).
тЗТ┬а2x┬атИИ┬а(0, ╧А)
тЗТ┬аSin(2x)> 0
тЗТ┬атАУSin(2x) < 0
тЗТ┬аfтАЩ(x)< 0
Hence, condition for f(x) to be decreasing
Thus f(x) is decreasing on interval┬а(0, ╧А/2).
Hence proved