Question

Cos 225°- sin 315°+ ctg 135° решите с помощью формулы приведения

Answer 1

Ответ:

Пошаговое объяснение:

=cos(180+45)-sin(360-45)+ctg(90+45)=-cos45+sin45-tg45=

V2/2 +V2/2 -1=2V2/2-1=V2-1  (V-корень)

Answer 2

To solve this trigonometric expression using the trigonometric addition/subtraction formulas, we'll first express all the angles in terms of standard angles (0°, 30°, 45°, 60°, and 90°).

1. Cosine (Cos) 225°: Since 225° is in the third quadrant, we can use the identity: cos(180° + θ) = -cos(θ)

cos(225°) = -cos(225° - 180°) = -cos(45°)

2. Sine (Sin) 315°: Since 315° is in the fourth quadrant, we can use the identity: sin(360° - θ) = sin(θ)

sin(315°) = sin(360° - 315°) = sin(45°)

3. Cotangent (Ctg) 135°: Since 135° is in the second quadrant, we can use the identity: cot(180° - θ) = -cot(θ)

ctg(135°) = -ctg(135° - 180°) = -ctg(-45°)

Now, we need to find the values of cos(45°), sin(45°), and cot(-45°).

Cosine and Sine of 45°: cos(45°) = sin(45°) = 1/√2 (These values are commonly known).

Cotangent of -45°: cot(-45°) = 1/tan(-45°) = 1/(-1) = -1

Now, let's substitute the values back into the expression:

Cos 225° - Sin 315° + Ctg 135° = -cos(45°) - sin(45°) - (-1) = -1/√2 - 1/√2 + 1 = 1 - 1/√2

To simplify the expression further, we can rationalize the denominator:

= (√2 - 1) / √2

Thus, the simplified value of the expression is (√2 - 1) / √2.