Evaluate the following expression. $$( 1 + \sin \alpha ) ( 1 - \sin \alpha )$$
A) $- \cos ^ { 2 } \alpha$
B) $\sin ^ { 2 } \alpha$
C) $\cos ^ { 2 } \alpha$
D) $- 2 \sin ^ { 2 } \alpha$
E) $2 \cos ^ { 2 } \alpha$

Question

Evaluate the following expression. $$( 1 + \sin \alpha ) ( 1 - \sin \alpha )$$ 
A) $- \cos ^ { 2 } \alpha$
B) $\sin ^ { 2 } \alpha$
C) $\cos ^ { 2 } \alpha$
D) $- 2 \sin ^ { 2 } \alpha$
E) $2 \cos ^ { 2 } \alpha$

Quizplus · Accepted Answer

This expression is an example of the difference of squares, $a^2 - b^2 = (a + b)(a - b)$. Here, $a = 1$ and $b = \sin \alpha$, so the expression simplifies to $1^2 - (\sin \alpha)^2 = 1 - \sin^2 \alpha$, which is equal to $\cos^2 \alpha$ by the Pythagorean identity.

Evaluate the Following Expression (1+sin⁡α)(1−sin⁡α)( 1 + \sin \alpha ) ( 1 - \sin \alpha )(1+sinα)(1−sinα)

Evaluate the Following Expression $( 1 + \sin \alpha ) ( 1 - \sin \alpha )$