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10 grade maths

How do you simplify (1 - cos x)(1 + cos x)?

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11 Months agoGrade
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1 Answer

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ApprovedApproved Tutor Answer11 Months ago

To simplify the expression (1 - cos x)(1 + cos x), we can use the difference of squares formula, which states that (a - b)(a + b) = a² - b².

Applying the Formula

In this case, let a = 1 and b = cos x. Therefore, we can rewrite the expression as:

(1 - cos x)(1 + cos x) = 1² - (cos x)²

Calculating the Result

Now, we calculate:

  • 1² = 1
  • (cos x)² = cos² x

Putting it all together, we have:

1 - cos² x

Final Simplification

Using the Pythagorean identity, we know that:

sin² x + cos² x = 1

This allows us to express 1 - cos² x as:

sin² x

Conclusion

Thus, the simplified form of (1 - cos x)(1 + cos x) is:

sin² x

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