Question

Sin^2*765градусов/1-cos*420градусов

Answer 1

Ответ:

1

Объяснение:

$\frac{sin^{2}(765)}{1-cos(420)}}$ = $\frac{(\frac{\sqrt{2} }{2} )^{2}}{1-\frac{1}{2} } =\frac{ \frac{1}{2} }{\frac{1}{2} } = 1$

1)sin(765°)=sin(45°+2×360°)=sin(45°)=√2/2

2)cos(420°)=cos(60°+360°)=cos(60°)=1/2

Answer 2

To evaluate the expression sin^2(765 degrees) / (1 - cos(420 degrees)), we can convert the angles to radians and then use the trigonometric identities. Here's the step-by-step solution:

Step 1: Convert degrees to radians. 765 degrees = (765 * π) / 180 ≈ 13.358 radians 420 degrees = (420 * π) / 180 ≈ 7.333 radians

Step 2: Apply the trigonometric identities. sin^2(x) = (1 - cos(2x)) / 2 cos(2x) = cos^2(x) - sin^2(x)

sin^2(765 degrees) = (1 - cos(2 * 13.358)) / 2 cos(2 * 13.358) = cos^2(13.358) - sin^2(13.358)

Step 3: Evaluate the expressions. cos(13.358) ≈ 0.9749 sin(13.358) ≈ 0.2225

cos(2 * 13.358) ≈ cos^2(13.358) - sin^2(13.358) ≈ 0.9749^2 - 0.2225^2 ≈ 0.9504

sin^2(765 degrees) ≈ (1 - 0.9504) / 2 ≈ 0.0248

Now let's evaluate the denominator:

cos(420 degrees) ≈ cos(7.333) ≈ 0.9985

Finally, substitute the values into the expression:

sin^2(765 degrees) / (1 - cos(420 degrees)) = 0.0248 / (1 - 0.9985) ≈ 0.0248 / 0.0015 ≈ 16.53

Therefore, sin^2(765 degrees) / (1 - cos(420 degrees)) is approximately equal to 16.53.