Question

Упростите выражения: 1) 1-cos^2 a; 2) 1+sin^2 a+cos^2 a

Answer 1

1) sin^2 a + cos^2 a = 1 следовательно:

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

2) по тому же принципу:

1 + sin^2 a + cos^2 a = 1 + (sin^2 a + cos^2 a) = 1 + 1 = 2

Answer 2

I can help you simplify trigonometric expressions using some identities and algebraic rules. Here are the steps for each expression:

1) 1 - cos^2 a Using the Pythagorean identity, sin^2 a + cos^2 a = 1, we can rewrite 1 as sin^2 a + cos^2 a and then subtract cos^2 a from both sides. This gives us:

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

So, 1 - cos^2 a simplifies to sin^2 a.

2) 1 + sin^2 a + cos^2 a Using the same Pythagorean identity, we can replace sin^2 a + cos^2 a with 1. This gives us:

1 + sin^2 a + cos^2 a = 1 + 1 = 2

So, 1 + sin^2 a + cos^2 a simplifies to 2.

If you want to learn more about how to simplify trigonometric expressions, you can watch some videos or read some web pages on this topic. I hope this helps. Have a nice day!how to simplify trigonometric expressions