Question

Величина sin(-7π/4)+cos(7π/4)+tg(15π/4)-ctg(-7π/4) равна

Answer 1

Ответ:√2-2

Пошаговое объяснение:

sin(-7π/4)+cos(7π/4)+tg(15π/4)-ctg(-7π/4)=

(-sin(7π/4))+((cos(2π-π/4))+(tg(4π-π/4))+ctg(2π-π/4)=

sin(π/4)+cos(π/4)-tg(π/4)-ctg(π/4)=√2/2+√2/2-1-1=√2-2

Answer 2

To calculate the value of the given expression, let's break it down step by step:

1. Find the value of sin(-7π/4): Using the periodicity property of sine, sin(x) = -sin(x + 2π), we can rewrite -7π/4 as -7π/4 + 2π = -π/4. Now, sin(-π/4) = -sin(π/4) = -√2/2.

2. Find the value of cos(7π/4): Using the periodicity property of cosine, cos(x) = cos(x + 2π), we can rewrite 7π/4 as 7π/4 - 2π = -π/4. Now, cos(-π/4) = cos(π/4) = √2/2.

3. Find the value of tan(15π/4): Using the periodicity property of tangent, tan(x) = tan(x + π), we can rewrite 15π/4 as 15π/4 - π = 11π/4. Now, tan(11π/4) = tan(π/4) = 1.

4. Find the value of cot(-7π/4): Using the periodicity property of cotangent, cot(x) = cot(x + π), we can rewrite -7π/4 as -7π/4 + π = -3π/4. Now, cot(-3π/4) = -cot(3π/4) = -(-1) = 1.

Now, the expression becomes: sin(-7π/4) + cos(7π/4) + tan(15π/4) - cot(-7π/4) = -√2/2 + √2/2 + 1 - 1 = 0.

So, the value of the given expression is 0.