Question

1+(tg^2(-a)-1/sin(0,5п+2а)

Answer 1

Решение задания приложено

Answer 2

To simplify the expression 1 + (tg^2(-a) - 1/sin(0.5π + 2a)), let's break it down step by step:

1. Starting with the innermost function, we have sin(0.5π + 2a). Since sin(π/2 + θ) = cos(θ), we can rewrite it as cos(2a):

1 + (tg^2(-a) - 1/cos(2a))

2. Next, we have tg^2(-a). Since tg(-θ) = -tan(θ), we can rewrite it as -tan^2(a):

1 + (-tan^2(a) - 1/cos(2a))

3. Now, we can combine the terms inside the parentheses:

1 - tan^2(a) - 1/cos(2a)

4. Using the trigonometric identity tan^2(a) + 1 = sec^2(a), we can simplify the expression further:

1 - sec^2(a) - 1/cos(2a)

5. Recall that sec(a) = 1/cos(a), so we can substitute it in:

1 - 1/cos^2(a) - 1/cos(2a)

6. Multiplying the first term by cos^2(a)/cos^2(a) to get a common denominator:

cos^2(a)/cos^2(a) - 1/cos^2(a) - 1/cos(2a)

7. Combining the terms over the common denominator:

(cos^2(a) - 1 - cos(2a))/cos^2(a)

This is the simplified form of the given expression: (cos^2(a) - 1 - cos(2a))/cos^2(a)