KEAM 2018 Math Paper

5‌cos‌θ+3‌cos(θ+‌

π

3

)+3
=‌

13

2

‌cos‌θ−‌

3√3

2

‌sin‌θ+3
Let ‌

13

2

=a and ‌

3√3

2

=b
Then expression becomes,
a‌cos‌θ−b‌sin‌θ+3
Maximum value of this type of expression is cqual to
[a2+b2]‌

1

2

+3= Maximum value
After putting values of a and b, we get
[49]‌

1

2

+3= Max value
10= Max value