Question

the maximum value of 2sintheta + 3costheta ?

Answer 1

Let 2 be r*cos(theta) and 3 be r*sin(theta) where r is a variable.

So, squaring and adding them, we have

13=r²(cos²(theta)+sin²(theta))

Or, r²=13…or, r=√13

Now the original qs changes as r*cos(theta)*sinx+r*sin(theta)*cosx….

Where r=√13

We can rewrite the equation using trigo formulas as

√13(sin((theta)+x))

So…max value of sin(anything) is 1…which means max value of √13*sin(anything) is √13

I hope it will help u