Question

(sin10°+cos10°)²-cos70°=?

Answer 1

(sin10°+cos10°)²-cos70°=sin²10°+2sin10°cos10°+cos²10°-cos70°=(sin²10+cos²10°)+2sin10°cos10°-cos70°=

выражение, стоящее в скобке, равно единице. Следующее слагаемое - это формула синуса двойного угла. Получим

=1+sin20°-cos70°=1+sin20°-cos(90°-20°)=1+sin20°-sin20°=1

Ответ: 1

Answer 2

Let's break down the expression step by step:

1. First, let's calculate sin(10°) and cos(10°):

sin(10°) ≈ 0.1736 cos(10°) ≈ 0.9848

2. Now, calculate (sin(10°) + cos(10°))^2:

(sin(10°) + cos(10°))^2 = (0.1736 + 0.9848)^2 ≈ (1.1584)^2 ≈ 1.3402

3. Next, let's calculate cos(70°):

cos(70°) ≈ 0.3420

4. Finally, subtract cos(70°) from the result in step 2:

(1.3402) - 0.3420 ≈ 0.9982

Therefore, (sin(10°) + cos(10°))^2 - cos(70°) ≈ 0.9982.