Answer:
Step-by-step explanation:
Given sin²∅ + sin∅ = 1, we are to find the value of sin²∅ + sin⁴∅. ... 2
From sin²∅ + sin∅. = 1; sin²∅ = 1 - sin∅. ... 3
Substitute equation 3 into 1
sin²∅ + sin⁴∅
= sin²∅ + (sin²∅)²
= (1 - sin∅)+( 1 - sin∅)²
open the parenthesis
= 1 - sin∅+ (1-2sin∅+ sin²∅)
= 1 - sin∅+ 1-2sin∅+ sin²∅
= 1+1-sin∅-2sin∅+sin²∅
= 2 - 3sin∅+sin²∅
Since sin²∅ = 1 - sin∅, the resulting equation becomes;
= 2 - 3sin∅+(1 - sin∅)
= 2 - 3sin∅+1-sin∅
= 3-4sin∅
