Question

1. Вычислите при помощи формул приведения: а) (cos 780 - ctg 495) sin 225 помогите со знаками. там потом меняется на +tg. почему вообще не понимаю. объясните пожалуйста подробно

Answer 1

$(Cos780^{o}-Ctg495^{o})*Sin225^{o}=[Cos(360^{o}*2+60^{o}-Ctg(180^{o}*2+135^{o})]*Sin(180^{o}+45^{o})=(Cos60^{0}-Ctg135^{o})*(-Sin45^{o})=(Cos60^{o}-Ctg(90^{o}+45^{o})*(-Sin45^{o})=(Cos60^{o}+tg45^{o})*(-Sin45^o})=(\frac{1}{2}+1)*(-\frac{\sqrt{2}}{2})=\frac{3}{2}*(-\frac{\sqrt{2}}{2}) =-\frac{3\sqrt{2}}{4}\\\\Otvet:\boxed{-\frac{3\sqrt{2}}{4}}$

По формулам приведения :

$Ctg(90^{o}+\alpha)=-tg\alpha$

Answer 2

#### Calculation using Reduction Formulas To calculate the expression **(cos 780 - ctg 495) sin 225**, we can use reduction formulas to simplify the trigonometric functions involved. Let's break down the steps: 1. Start with the expression **(cos 780 - ctg 495) sin 225**. 2. Apply the reduction formula for cosine: **cos(π - θ) = -cos(θ)**. Since 780 degrees is equivalent to 780 - 360 = 420 degrees, we can rewrite the expression as **(-cos 420 - ctg 495) sin 225**. 3. Apply the reduction formula for cotangent: **ctg(θ) = 1/tan(θ)**. Therefore, **ctg 495 = 1/tan 495**. 4. Apply the reduction formula for sine: **sin(π - θ) = sin(θ)**. Since 225 degrees is equivalent to 225 - 180 = 45 degrees, we can rewrite the expression as **(-cos 420 - 1/tan 495) sin 45**. 5. Apply the reduction formula for tangent: **tan(θ) = sin(θ)/cos(θ)**. Therefore, **1/tan 495 = cos 495 / sin 495**. 6. Substitute the values obtained from the reduction formulas into the expression: **(-cos 420 - cos 495 / sin 495) sin 45**. 7. Simplify the expression further if needed. Please note that the reduction formulas used here are standard trigonometric identities. The specific values of the trigonometric functions at 420, 495, and 45 degrees can be calculated using a calculator or trigonometric tables. Unfortunately, the search results did not provide specific snippets related to the calculation of this expression. However, the steps outlined above should help you simplify the expression using reduction formulas.