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a cos θ + $b$ sin θ = 4 and a sin θ − $b$ cos θ = 3. Find $a^{2} + b^{2}$ .

Competition practiceTrigonometry

A25
B7
C5
D1

Step-by-Step Solution

Square and add:

a^{2}

(co

s^{2}

θ + si

n^{2}

θ) +

b^{2}

(si

n^{2}

θ + co

s^{2}

θ) + (cross terms cancel) = 16 + 9, so

a^{2} + b^{2} = 25

.

Answer: A) 25

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