Simplify: (1 - θ)(1 + θ).

Correct Answer is : cos⁡2θ² θcos2θ

Correct Answer is : cos⁡2θ² θcos2θ

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WAEC Further Mathematics 2014 Paper

Question : 2

Total: 40

Simplify:

(1 - \sin \theta)(1 + \sin \theta)

Solution:

Concept:

Use the identity

\sin^{2} \theta + \cos^{2} \theta = 1

and the difference of squares expansion.

Explanation:

Expand

(1 - \sin \theta)(1 + \sin \theta)

using

(a-b)(a+b) = a^{2} - b^{2}

Here,

a = 1

and

b = \sin \theta

So,

(1 - \sin \theta)(1 + \sin \theta) = 1^{2} - \sin^{2} \theta = 1 - \sin^{2} \theta

From the Pythagorean identity,

1 - \sin^{2} \theta = \cos^{2} \theta

Therefore, the simplified expression is

\cos^{2} \theta

Answer:

\cos^{2} \theta

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