Question

Simplify:
tan² θ cos² - sin² θ

can anyone write the steps? many thanks! ​

Answer 1

The given expression simplifies to zero.

Explanation:

Tangent Trigonometric Identity:

`\boxed{\tan \theta=(\sin \theta)/(\cos \theta)}`

Given expression:

`\tan^2 \theta \cos^2 \theta - \sin^2 \theta`

To simplify the given expression, rewrite tan²θ using the tan trigonometric identity:

`\implies (\sin^2 \theta)/(\cos^2 \theta) \cdot \cos^2 \theta - \sin^2 \theta`

`\implies (\sin^2 \theta \cos^2 \theta)/(\cos^2 \theta) - \sin^2 \theta`

Cancel the common factor cos²θ:

`\implies \sin^2 \theta - \sin^2 \theta`

Add similar elements:

`\implies \sin^2 \theta - \sin^2 \theta=0`

Therefore, the given expression simplifies to zero.