Question

If sin²∅ + sin∅ = 1 , then what is the value of sin²∅ + sin⁴∅.​

Answer 1

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∅