Question

Cos²Π/4+sin5Π/6-tgΠ/4

Answer 1

$cos^2(\frac{\pi}{4})+sin\frac{5\pi}{6} -tg\frac{\pi}{4}=(\frac{\sqrt{2} }{2})^2+\frac{1}{2} -1=\frac{1}{2}+ \frac{1}{2}-1=1-1=0$

Answer 2

cos²(π/4)+sin(5π/6)-tg(π/4)=(√2/2)²+1/2-1=1/2+1/2-1=1-1=0.

Answer 3

Let's simplify the expression step by step:

1. cos²(π/4): cos(π/4) = √2 / 2 cos²(π/4) = (√2 / 2)² = 2 / 4 = 1 / 2

2. sin(5π/6): sin(5π/6) = sin(π - π/6) = sin(π/6) = 1 / 2

3. tan(π/4): tan(π/4) = 1

Now, let's plug these values back into the original expression:

cos²(π/4) + sin(5π/6) - tan(π/4) = 1/2 + 1/2 - 1

Combine like terms:

1/2 + 1/2 = 1

So, the final simplified expression is:

1 - 1 = 0