Question

Simplify (1 − cos x)(1 + cos x). (2 points)

Answer 1

Answer:

sin²x

Step-by-step explanation:

we have

(1 − cos x)(1 + cos x)=1-cos²x

Remember that

sin²x+cos²x=1 ------> i-cos²x=sin²x

therefore

(1 − cos x)(1 + cos x)=sin²x

Answer 2

Answer:

$sin^2x$

Step-by-step explanation:

Given expression,

$(1 - cos x)(1 + cos x)$

By using $a^2-b^2=(a+b)(a-b)$

$(1 - cos x)(1 + cos x)=1^2 - cos^2x = 1 - cos^2x$

$\because sin^2x+cos^2x=1$

$\implies (1 - cos x)(1 + cos x)=sin^2x+cos^2x - cos^2x=sin^2x$

Since, further simplification is not possible,

Hence, the simplified form of the given expression is $sin^2x$