# CAT Practice : Trigonometry

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Max and Min value of the given expression

## Maximum and Minimum Value

Q.4: Find the maximum and minimum value of 8 cos A + 15 sin A + 15
1. 11√2+15; 15
2. 30; 8
3. 32; -2
4. 23; 8

Choice C. 32; -2

## Detailed Solution

Always look out for Pythagorean triplets, we know that (8,15,17) is one
∴ 17 ($\frac{8}{17} cos⁡ A +\frac{15}{17}sinA)$
Let there be a angle B for which sin B = $\frac{8}{17}, cos B = \frac{15}{17}$
=) 17( sin B cos A + cos B sin A) + 15
17(sin(A+B)) + 15
We know that sin(A+B)max = 1
sin(A+B)min = -1
∴ Max value = 17x1 +15 = 32
Min value = 17 x -1 + 15 = -2

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