Question

Sin(4л - x) : cos(270° - x) + cos(п+ х) : sin(270° + х) - 1.​

Answer 1

Sin(4П-х)*cos(270-x)+cos(П+х)*sin(270+x)-1=-sin x*(-sin x)+(-cos x)*(-cos x)-1=sin^2 x+cos^2 x-1=1-1=0

Answer 2

To simplify the given expression, we can use trigonometric identities to rewrite the trigonometric functions in terms of sine and cosine functions. Let's start by simplifying each part of the expression:

1. Sin(4π - x) : cos(270° - x): We can use the identity sin(π - θ) = sin(θ) and cos(π - θ) = -cos(θ) to rewrite sin(4π - x) and cos(270° - x) as follows:

   sin(4π - x) = sin(-x) cos(270° - x) = -cos(x)

2. Cos(π + x) : sin(270° + x): We can use the identity cos(π + θ) = -cos(θ) and sin(π + θ) = -sin(θ) to rewrite cos(π + x) and sin(270° + x) as follows:

   cos(π + x) = -cos(x) sin(270° + x) = -sin(x)

Now, let's substitute these simplifications back into the original expression:

(sin(-x) : (-cos(x))) + (-cos(x) : (-sin(x))) - 1

Now, we can simplify further:

(sin(-x) / (-cos(x))) + (-cos(x) / (-sin(x))) - 1

Now, remember that sin(-x) = -sin(x) and cos(-x) = cos(x):

(-sin(x) / (-cos(x))) + (-cos(x) / (-sin(x))) - 1

Now, we have negative signs in both the numerator and denominator of the fractions, which can be canceled out:

(sin(x) / cos(x)) + (cos(x) / sin(x)) - 1

Now, we can simplify the fractions:

tan(x) + cot(x) - 1

So, the simplified expression for sin(4π - x) : cos(270° - x) + cos(π + x) : sin(270° + x) - 1 is:

tan(x) + cot(x) - 1