Question

Sin700°/cos²35°-sin²35°​

Answer 1

Ответ:

-1

Объяснение:

Сперва sin700 превращаем на -sin20°.

А -sin20° превращаем на -cos70°.

Снизу мы используем формулу:

cos2x = cos²x - sin²x

Answer 2

To calculate the value of sin(700°) / (cos²(35°) - sin²(35°)), we can break it down step by step:

1. Calculate sin(700°): sin(700°) is equivalent to sin(700° - 360°) because sin function has a periodicity of 360°. So, sin(700°) = sin(700° - 2 * 360°) = sin(700° - 720°) = sin(-20°) because sin(-20°) has the same value as sin(20°). sin(20°) is the positive value for sine, and its value is √3/2.

2. Calculate cos²(35°) and sin²(35°): cos(35°) and sin(35°) can be calculated directly. You can use the trigonometric identity: cos²(θ) + sin²(θ) = 1

   So, cos²(35°) = 1 - sin²(35°)

3. Substitute these values into the original expression:

   sin(700°) / (cos²(35°) - sin²(35°)) = (√3/2) / (1 - sin²(35°) - sin²(35°)) = (√3/2) / (1 - 2 * sin²(35°))

Now, you need to find sin²(35°). Use the trigonometric identity:

sin(2θ) = 2sin(θ)cos(θ)

sin(35°) = sin(2 * 17.5°) = 2 * sin(17.5°) * cos(17.5°)

The exact values of sin(17.5°) and cos(17.5°) are not common values, but you can use a calculator to find these values. Once you have sin(17.5°), you can find sin(35°) and then sin²(35°).

Finally, substitute the value of sin²(35°) into the expression:

(√3/2) / [1 - 2 * sin²(35°)]

Remember that this answer will be in terms of sin(17.5°) and cos(17.5°), which you can calculate using a calculator or a trigonometric table.