Answered

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(tan2x +1) (cos²x -1)

Simplify please

Sagot :

hanifgibrin69

Step-by-step explanation:

Let's simplify the expression:

(tan2x + 1)(cos²x - 1)

= (tan2x + 1)(cos²x - 1) (using the distributive property)

= tan2x * cos²x - tan2x * 1 + 1 * cos²x - 1 * 1

= tan2x * cos²x - tan2x + cos²x - 1

Now, let's simplify the terms:

tan2x * cos²x = tan2x * (1 - sin²x) (using the trigonometric identity)

= tan2x - tan2x * sin²x

= tan2x - (sin²x * tan2x)

= tan2x - sin²x * tan2x

Now, we can combine like terms:

tan2x - sin²x * tan2x = tan2x(1 - sin²x)

= tan2x * cos²x

So, the simplified expression is:

tan2x * cos²x - tan2x + cos²x - 1

= (tan2x * cos²x) - (tan2x) + (cos²x) - 1

= (tan2x * cos²x) - (tan2x) + (cos²x) - 1

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