IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

joyfrancis

The second question becomes pretty confusing when you try to analyse the values so it is better to make the graph.

see,

y=2sinx+cosx

multiply and divide by

5

y=[2sinx/

5 + cosx/

5]

5

Let cos2/

5 = a

y=sin(a+x)

To make the graph of sin(a+x) make the graph of sinx and shift it backwards by a distance of cos inverse 2/

5.

Now you can get the intervals of monotonocity of the function.

I am getting

Increasing --> (-a,90-a)U(135-a,45+a))

Decreasing-->(90-a,135-a)

Correct me if i'm wrong!