Find the maximum and minimum value of 8 cos A + 15 sin A + 15a)11√2+15; 15b)30; 8c)32; -2d)23; 8Correct answer is option 'C'. Can you explain this answer?

Question

Find the maximum and minimum value of 8 cos A + 15 sin A + 15a)11&radic;2+15; 15b)30; 8c)32; -2d)23; 8Correct answer is option 'C'. Can you explain this answer?

Answer

To find the maximum and minimum value of the expression 8 cos A + 15 sin A + 15, we can rewrite it as a single trigonometric function using the trigonometric identity:

a cos A + b sin A = √(a^2 + b^2) sin(A + α), where tan α = b/a.

In this case, a = 8, b = 15, and α = tan^(-1)(15/8).

Using these values, we can rewrite the expression as:

8 cos A + 15 sin A + 15 = √(8^2 + 15^2) sin(A + α) + 15
= √(64 + 225) sin(A + α) + 15
= √289 sin(A + α) + 15
= 17 sin(A + α) + 15

Since sin(A + α) has a maximum value of 1 and a minimum value of -1, the expression 17 sin(A + α) + 15 will have a maximum value of 17 + 15 = 32 and a minimum value of -17 + 15 = -2.

Therefore, the maximum value of 8 cos A + 15 sin A + 15 is 32, and the minimum value is -2.

Answer

(c) 32,-2.

maximum and minimum value of 8 COSA +15 SINA is + and- (under root { 8^2+15^2})

Answer

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