Question

Sin 69° cos 21° + sin 21 cos 69t°

Answer 1

Відповідь:

sin(69+21)

Покрокове пояснення:

sin(x + y) = sinx cosy + cosx siny

sin(69+21) = sin 69cos21 + sin21cos69

Answer 2

To evaluate the expression, we'll use the trigonometric identities:

1. $\sin(\alpha + \beta) = \sin(\alpha)\cos(\beta) + \cos(\alpha)\sin(\beta)$
2. $\sin(90° - \theta) = \cos(\theta)$
3. $\cos(90° - \theta) = \sin(\theta)$

We'll first simplify the expression step by step:

1. $\sin(69°)\cos(21°) + \sin(21°)\cos(69°)$

2. $\sin(69°)\cos(21°) + \cos(90° - 69°)\cos(21°)$ [Using identity 3]

3. $\sin(69°)\cos(21°) + \sin(69°)\cos(21°)$ [Using identity 2]

4. $2\sin(69°)\cos(21°)$

Now, let's use a calculator to find the values of $\sin(69°)$ and $\cos(21°)$:

$\sin(69°) \approx 0.897$ $\cos(21°) \approx 0.939$

Finally, substitute these values into the expression:

$2 \times 0.897 \times 0.939 \approx 1.680$

So, the value of the expression is approximately 1.680.