Question

2sin^2a-1+cos^2a+(1-sina)(1+sina)​

Answer 1

Ответ:

1

Объяснение:

2sin²a-1+cos²a+(1-sina)(1+sina)​=2sin²a-1+cos²a+1-sin²a=

=2sin²a-sin²a-1+1+cos²a=sin²a+cos²a=1

Answer 2

To simplify the expression 2sin^2(a) - 1 + cos^2(a) + (1 - sin(a))(1 + sin(a)), you can use trigonometric identities to rewrite and simplify it. Here's the step-by-step solution:

1. Use the Pythagorean trigonometric identity: sin^2(a) + cos^2(a) = 1.

2. Replace cos^2(a) in the expression with 1 - sin^2(a) using the Pythagorean identity:

2sin^2(a) - 1 + 1 - sin^2(a) + (1 - sin(a))(1 + sin(a))

3. Now, distribute the terms in the last part of the expression:

2sin^2(a) - 1 + 1 - sin^2(a) + (1 - sin^2(a))

4. Combine like terms:

(2sin^2(a) - sin^2(a) - sin^2(a)) + (1 - 1) + (1 - sin^2(a))

5. Further simplify:

(sin^2(a)) + (0) + (1 - sin^2(a))

6. Now, simplify the expression:

sin^2(a) + 1 - sin^2(a)

7. The sin^2(a) and -sin^2(a) terms cancel each other out:

1

So, the simplified expression is 1.