Simplify (1-sin(t))(1+sin(t))

Problem

(1−sin(t))*(1+sin(t))

Solution

1. Recognize the pattern as a difference of squares, which follows the algebraic identity (a−b)*(a+b)=a2−b2

2. Apply the identity by setting a=1 and b=sin(t)

(1−sin(t))*(1+sin(t))=1−sin2(t)

3. Simplify the constants by calculating 1

1−sin2(t)

4. Apply the Pythagorean identity sin2(t)+cos2(t)=1 which implies 1−sin2(t)=cos2(t)

cos2(t)

Final Answer

(1−sin(t))*(1+sin(t))=cos2(t)

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