Find the value of sin⁶θ + cos⁶θ + 3 sin²θ cos²θ.

1. a³ + b³ + 3ab(a + b) = (a + b)³ with a = sin²θ, b = cos²θ and a + b = 1, so the value is 1.

Find the value of si $n^{6}$ θ + co $s^{6}$ θ + 3 si $n^{2}$ θ co $s^{2}$ θ.

Competition practiceTrigonometry

a^{3} + b^{3} + 3 ab (a + b) = (a + b)^{3}

with

a

= si

n^{2}

θ,

b

= co

s^{2}

θ and

a + b = 1

, so the value is 1.

Answer: A) 1

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