Simplify Tan(180+theter)*cos(90+theter)+sin(360-theter)*tan(180-theter) thanks
that's theta, not theter.
tan(180+θ)*cos(90+θ) + sin(360-θ)*tan(180-θ)
= (tanθ)(-sinθ) + (-sinθ)(-tanθ)
= 0
It's worth 5 marks how did u get =0
To simplify the given expression, we can start by using the trigonometric identities to rewrite the trigonometric functions. Let's break it down step by step:
1. Tan(180 + θ) can be rewritten as Tan(180) * Tan(θ). (The tangent function has a period of 180 degrees, so adding or subtracting any multiple of 180 degrees will not affect its value.)
2. Cos(90 + θ) can be rewritten as -Sin(θ). (This is a complementary angle identity where the cosine of the complement of an angle is equal to the sine of the angle itself.)
3. Sin(360 - θ) can be rewritten as -Sin(-θ) or Sin(θ). (The sine function has a period of 360 degrees, so subtracting or adding any multiple of 360 degrees will not affect its value.)
4. Tan(180 - θ) can be rewritten as -Tan(θ). (The tangent function has a period of 180 degrees, so subtracting or adding any multiple of 180 degrees will not affect its value.)
Now, let's substitute these rewritten forms into the original expression:
Tan(180 + θ) * Cos(90 + θ) + Sin(360 - θ) * Tan(180 - θ)
= Tan(180) * Tan(θ) * (-Sin(θ)) + Sin(θ) * (-Tan(θ))
= -Tan(θ) * Sin(θ) + Sin(θ) * (-Tan(θ))
= -2 * Tan(θ) * Sin(θ)
So, the simplified expression is -2 * Tan(θ) * Sin(θ).