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Simplifying expressionsAlgebraHigh schoolabout 0:51

Simplify 1 - sin(x)^2: animated lesson

A narrated, step-by-step simplifying expressions video lesson with captions. Final answer: cos²(x).

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Transcript

Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.3 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
$1-{\sin\left( x\right)}^{2}$
2. Step by step
1. Rewrite everything in terms of sin x and cos x
2. $-\sin^{2} x + 1$
  Combine into a single fraction
3. $-\sin^{2} x + 1$
  Use sin²x + cos²x = 1 (replace cos² with 1 − sin²) and cancel common factors
4. $-\sin^{2} x + 1 = \cos^2x$
  Recognise a standard form
3. The answer
$\cos^2x$
1 - sin(x)^2 = cos²(x)
4. Check
- Numeric spot check: the original expression and the result agree at sample values of x.

Transcript

The problem. Here is the problem: 1 minus sin(x) squared. Simplify a trigonometric expression.

Step by step. Rewrite everything in terms of sin x and cos x. The expression already uses only sine and cosine. Combine into a single fraction. Use sin squaredx plus cos squaredx equals 1 (replace cos squared with 1 minus sin squared) and cancel common factors. Recognise a standard form. Cross-multiplying and reducing with sin squared plus cos squared equals 1 shows the difference is exactly 0.

The answer. So the answer is cos squared(x). 1 minus sin(x) squared simplifies to cos squared(x) for every x where the original expression is defined.

Check. Numeric spot check: the original expression and the result agree at sample values of x.

About simplifying expressions

Simplify algebraic and rational expressions by collecting like terms and cancelling common factors.

Simplify 1 - sin(x)^2: Animated Step-by-Step Lesson