Question

Cos105cos5+sin105cos85/sin95cos5-cos95sin185. Почему получается -tg70? Объясните пожалуйста

Answer 1

= (Cos105cos5+sin105cos(90-5)) /(sin95cos5-cos95sin(180+5))=
={Cos105cos5+sin105sin5) / (sin95cos5+cos95sin5)=
=cos(105-5)/sin(95+5)=
=cos100/sin100=ctg100=ctg(90+10)=
=-tg10.

Answer 2

Calculating Trigonometric Expression

To calculate the given trigonometric expression cos(105)cos(5)+sin(105)cos(85)/sin(95)cos(5)-cos(95)sin(185) and understand why it simplifies to -tan(70), let's break it down step by step.

First, let's simplify the expression using trigonometric identities and then evaluate it.

Simplifying the Expression

We can simplify the given expression step by step using trigonometric identities:

1. cos(105)cos(5) + sin(105)cos(85) / sin(95)cos(5) - cos(95)sin(185)

2. Using the identity sin(a)cos(b) = (1/2)[sin(a+b) + sin(a-b)]: cos(105)cos(5) + (1/2)[sin(190) + sin(20)] / sin(95)cos(5) - (1/2)[sin(90) - sin(280)]

3. Simplifying further: cos(105)cos(5) + (1/2)[0 + sin(20)] / sin(95)cos(5) - (1/2)[1 - 0]

4. Now, evaluating the trigonometric functions: cos(105) ≈ -0.258819, cos(5) ≈ 0.996195, sin(20) ≈ 0.912945, sin(95) ≈ 0.996195

5. Substituting the values: -0.258819 * 0.996195 + 0.5 * 0.912945 / 0.996195 * 0.996195 - 0.5 * 1

6. Simplifying further: -0.2577 + 0.4565 / 0.996195 - 0.5

7. Evaluating the expression: -0.2577 + 0.4565 / 0.496195 - 0.5 ≈ 0.1988 / -0.003805 ≈ -52.21

Conclusion

After evaluating the given expression, it simplifies to approximately -52.21, not -tan(70). It seems there might be a mistake in the original expression or the expected result. If you have a different expression or expected result in mind, please provide it so I can assist you further.