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If sin θ + si $n^{2}$ θ = 1, find co $s^{12}$ θ + 3co $s^{10}$ θ + 3co $s^{8}$ θ + co $s^{6}$ θ + 2.

Competition practiceTrigonometry

A3
B2
C1
D4

Step-by-Step Solution

sin θ

= 1 - s i

n^{2}

θ =

co

s^{2}

θ. The first four terms are

(co s^{4} θ + co s^{2} θ)^{3} = (s i n^{2} θ + s in θ)^{3} = 1^{3} = 1

, so the total is 1 + 2 = 3.

Answer: A) 3

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