Question

1) cos²a 1-sin²a 2)1-2sin²a 2cos²a-1​

Answer 1

Решение задания прилагаю

Answer 2

Let's simplify the given expressions:

1. cos²(a) - 1 - sin²(a)

Using the trigonometric identity cos²(a) + sin²(a) = 1, we can simplify this expression:

cos²(a) - 1 - sin²(a) = 1 - 1 - sin²(a) = -sin²(a)

2. 1 - 2sin²(a) / (2cos²(a) - 1)

Let's work on simplifying the denominator first:

2cos²(a) - 1 = 2(cos²(a) - 1/2)

Now, let's use the trigonometric identity sin²(a) + cos²(a) = 1 to express cos²(a) in terms of sin²(a):

cos²(a) = 1 - sin²(a)

Substitute this into the denominator:

2(cos²(a) - 1/2) = 2((1 - sin²(a)) - 1/2) = 2(1 - sin²(a) - 1/2)

Now, let's simplify the entire expression:

1 - 2sin²(a) / (2cos²(a) - 1) = 1 - 2sin²(a) / (2(1 - sin²(a) - 1/2)) = 1 - 2sin²(a) / (2 - 2sin²(a) - 1)

Now, combine like terms in the denominator:

1 - 2sin²(a) / (2 - 2sin²(a) - 1) = 1 - 2sin²(a) / (1 - 2sin²(a))

So, the simplified expression is:

1 - 2sin²(a) / (1 - 2sin²(a))