Question

Find the maximum value of 5cosA + 12sinA + 12

Answer 1

= 5 * cos 90 + 12 * sin 0 + 12
= 5 * 1 + 12 * 1 + 12
= 5 +12 + 12
= 24 + 5
= 29 ans.

Answer 2

5cosA +12sinA + 12
= 13(5/13 cosA +12/13sinA) + 12
Now, for any values of B we can get sinB = 5/13
and we can replace cosB = 12/13. 
 We see that our assumption is right because we satisfy the condition sin^2B + cos^2B = 1
so we get 13(sinBcosA +cosBsinA) + 12...