Question

Solve for the following equation for 0°≤∅≤360°
1 + sin∅cos²∅ = sin∅

Answer 1

Step-by-step explanation:

Given :-

1 + Sin∅ Cos^2∅ = Sin∅

To find:-

Solve for the following equation for 0°≤∅≤360° ,

1 + Sin∅Cos^2∅ = Sin∅

Solution:-

Given that

1 + Sin∅Cos^2∅ = Sin∅

We know that

Sin^2 A + Cos^2 A = 1

Cos^2 A = 1-Sin^2 A

=> 1+ Sin∅(1-Sin^2∅) = Sin∅

=> 1+ Sin∅- Sin∅ Sin^2∅ = Sin∅

=> 1+ Sin∅- Sin^3∅ = Sin∅

=>1+ Sin∅- Sin^3∅ - Sin∅ = 0

=> 1- Sin^3∅ = 0

=> Sin^3∅ = 1

=> Sin∅ = 1

=> Sin ∅ = Sin 90°

=> ∅ = 90°

Answer:-

The value of ∅ for the given problem is 90°

Used formulae:-

• Sin^2 A + Cos^2 A = 1

• Sin 90° = 1