Question

2*sin99°*cos351°-2*sin351°*sin91°+16*sin15°*sin75°=​

Answer 1

Ответ:

Объяснение:=2·sin(90+9)·cos(360-9)-2sin(360-9)·sin(90+1)+16sin15·sin(90-15)= 2cos9·cos9 - (- 2sin9)·cos1 +

16sin15·cos15=2cos²9+2sin9·cos1+8sin30=1+cos18+sin8+sin10+4=

5+cos18+sin8+sin10. (условие какое и верно ли?)

Answer 2

To calculate the value of the expression, let's break it down step by step:

1. First, let's simplify the trigonometric functions using the trigonometric identities:

   • sin(99°) = sin(180° - 99°) = sin(81°)
   • cos(351°) = cos(360° - 351°) = cos(9°)
   • sin(351°) = sin(360° - 351°) = sin(9°)
   • sin(91°) = sin(90° + 1°) = sin(1°)
   • sin(15°) = sin(45° - 30°) = sin(45°)cos(30°) - cos(45°)sin(30°) = (√2/2)(√3/2) - (√2/2)(1/2) = √6/4 - √2/4 = (√6 - √2)/4
   • sin(75°) = sin(45° + 30°) = sin(45°)cos(30°) + cos(45°)sin(30°) = (√2/2)(√3/2) + (√2/2)(1/2) = √6/4 + √2/4 = (√6 + √2)/4

2. Substitute the simplified trigonometric values into the expression: 2sin(99°)cos(351°) - 2sin(351°)sin(91°) + 16sin(15°)sin(75°) = 2sin(81°)cos(9°) - 2sin(9°)sin(1°) + 16((√6 - √2)/4)((√6 + √2)/4)

3. Evaluate the trigonometric functions: sin(81°) ≈ 0.988, cos(9°) ≈ 0.987, sin(9°) ≈ 0.156, sin(1°) ≈ 0.017

4. Substitute the approximate values into the expression: ≈ 2 * 0.988 * 0.987 - 2 * 0.156 * 0.017 + 16 * ((√6 - √2)/4) * ((√6 + √2)/4)

5. Simplify and calculate the result: ≈ 1.939 - 0.053 + 16 * ((√6 - √2)/4) * ((√6 + √2)/4) ≈ 1.939 - 0.053 + 16 * ((6 - 2)/16) ≈ 1.939 - 0.053 + 4 ≈ 5.939

Therefore, 2*sin(99°)cos(351°) - 2sin(351°)sin(91°) + 16sin(15°)*sin(75°) ≈ 5.939.