Respuesta :

Answer is: b) 
How: Re-arrange formulae knowing tan(theta) = sin(theta)/cos(theta)
such that it become: cos(theta) -sin(theta)/cos(theta) x cos(theta) = 0.
From there; cos (theta) = sin(theta) (by re-arranging). Now, substitute figures of b), pie/4 = 45 degrees. At 45 degrees, sin(45) = cos(45) = 1/square root of 2. Also, 5pie/4 = 235 degrees. At 235 degrees, sin(235) = cos(235) = -1/square root of 2
Louli
Answer:
b. [tex] \frac{ \pi }{4} or \frac{5 \pi }{4} [/tex]

Explanation:
Before we begin, remember that:
tan α = [tex] \frac{sin \alpha }{cos \alpha } [/tex] 

Now for the given, we have:
cos θ - tan θ * cos θ = 0
cos θ - [tex] \frac{sin theta }{cos theta } [/tex] * cos θ = 0
cos θ - sin θ = 0
cos θ = sin θ
Now, divide both sides by cos θ, we get:
1 = tan θ

Following the ASTC rule, we know that the tan function is positive in the first and third quadrants.
This means that:
either θ = [tex] \frac{ \pi }{4} [/tex]

or θ = π + [tex] \frac{ \pi }{4} [/tex] = [tex] \frac{ 5 \pi }{4} [/tex]

Hope this helps :)

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