Question

Ctg n/2+5 sin n/3-cos 45°-1/2 tg 30°

Answer 1

Ответ:

а) 2sin30+cos45=2* \frac{1}{2}+\frac {\sqrt{2}}{2}= \frac{2+ \sqrt{2} }{2}    

б) tg \frac{ \pi }{3} - \frac{1}{3} ctg \frac{\pi}{6} = \sqrt{3}- \frac{1}{3}* \sqrt{3}=\frac{3 \sqrt{3}-\sqrt{3}}{3} =\frac{2\sqrt{3}}{3}    

в) 3cos\frac{\pi}{3}-2tg45=3*\frac{1}{2}-2*1=\frac{3-4}{2}=-0,5

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Пошаговое объяснение:

Answer 2

To simplify the expression, let's first express the trigonometric functions in their respective values:

1. Since the expression contains trigonometric functions like sine, cosine, and tangent, let's convert the angles into radians, as trigonometric functions usually work with radians:

   • cos(45°) = cos(45° * π/180) = cos(π/4)
   • tan(30°) = tan(30° * π/180) = tan(π/6)

2. Now, we'll simplify the expression step by step: Given expression: ctg(n/2) + 5sin(n/3) - cos(45°) - 1/2 * tan(30°)

   • ctg(n/2) is the cotangent function. We can rewrite it as 1/tan(n/2): 1/tan(n/2) + 5sin(n/3) - cos(π/4) - 1/2 * tan(π/6)

   • tan(n/2) can be expressed as sin(n)/[1 + cos(n)] (half-angle identity for tangent): 1/[sin(n)/[1 + cos(n)]] + 5sin(n/3) - cos(π/4) - 1/2 * tan(π/6)

   • Invert the fraction: (1 + cos(n))/sin(n) + 5sin(n/3) - cos(π/4) - 1/2 * tan(π/6)

   • Simplify the middle term: (1 + cos(n))/sin(n) + 5sin(n)/3 - cos(π/4) - 1/2 * tan(π/6)

   • The next step would depend on the value of 'n' (i.e., whether 'n' is a specific angle or a variable). If 'n' is a specific angle, you can plug in its value to get a numerical result. If 'n' is a variable, the expression remains as it is.

If you have a specific value for 'n', feel free to substitute it into the expression to get a numerical result. Otherwise, this is the simplified form of the expression.