Question

(sinx+cosx)(sinx-cosx)-sin^2

Answer 1

Ответ:

-cos^2(x)

Пошаговое объяснение:

На фото.

Применили формулу разности квадратов и сложили подобные. Синус квадрат икс самоуничтожился.

Answer 2

Let's simplify the given expression step by step:

Expression: (sinx + cosx)(sinx - cosx) - sin^2x

Step 1: Expand the brackets Using the distributive property, we can expand the expression:

(sin x + cos x)(sin x - cos x) = sin^2 x - cos^2 x

Step 2: Substitute the expansion Now, we substitute the expansion back into the original expression:

(sin x + cos x)(sin x - cos x) - sin^2 x = (sin^2 x - cos^2 x) - sin^2 x

Step 3: Combine like terms Next, combine like terms by adding and subtracting them:

(sin^2 x - cos^2 x) - sin^2 x = sin^2 x - cos^2 x - sin^2 x

Step 4: Simplify Finally, we can simplify further:

sin^2 x - cos^2 x - sin^2 x = -cos^2 x

So, the simplified expression is -cos^2 x.