Question

Cos^4(15°)-sin^4(15°)​

Answer 1

Ответ: √3/2

Объяснение:

cos⁴15°-sin⁴15°=(cos²15°-sin²15°)(cos²15°+sin²15°)=cos2*15° *1=cos30°=√3/2.

Answer 2

To evaluate the expression cos^4(15°) - sin^4(15°), we'll need to first find the values of cos(15°) and sin(15°) and then proceed with the calculation.

Step 1: Find cos(15°) and sin(15°) using trigonometric identities. We can use the half-angle formulas for sine and cosine to calculate these values.

cos(15°) = √[(1 + cos(30°)) / 2] sin(15°) = √[(1 - cos(30°)) / 2]

Step 2: Calculate cos^4(15°) and sin^4(15°).

cos^4(15°) = [cos(15°)]^4 sin^4(15°) = [sin(15°)]^4

Step 3: Substitute the values from Step 1 into Step 2.

cos^4(15°) = [√[(1 + cos(30°)) / 2]]^4 sin^4(15°) = [√[(1 - cos(30°)) / 2]]^4

Step 4: Calculate the values of cos^4(15°) and sin^4(15°).

Now, let's proceed with the calculations using a calculator:

cos(30°) = √3/2 cos(15°) = √[(1 + √3/2) / 2] ≈ 0.991445 sin(15°) = √[(1 - √3/2) / 2] ≈ 0.130526

cos^4(15°) ≈ (0.991445)^4 ≈ 0.964632 sin^4(15°) ≈ (0.130526)^4 ≈ 0.000287

Step 5: Finally, evaluate cos^4(15°) - sin^4(15°).

cos^4(15°) - sin^4(15°) ≈ 0.964632 - 0.000287 ≈ 0.964345

So, cos^4(15°) - sin^4(15°) ≈ 0.964345.