Answer to Question #144313 in Trigonometry for Shahir Sheikh

Question

Garett is attempting to verify this trig identity. He makes a mistake on one of the lines below. Which line has his first mistake?

sec(θ)−sin(θ)tan(θ)=cos(θ)

1.1cos(θ)−sin(θ)1(sin(θ)cos(θ))=cos(θ)

2. 1cos(θ)−sin(θ)cos(θ)=cos(θ)

3. 1−sin(θ)cos(θ)=cos(θ)

4. cos(θ)=cos(θ)

Answer 1

3. $1- sin\theta cos\theta \neq cos\theta\\$

Garette made a mistake on line 3. The equation gives two different results depending on which side being dealt with

$1- sin\theta cos\theta = \\ 1 - \dfrac{sin2\theta}{2}= \\ (cos^2\theta + sin^2\theta) - tan\theta\cos^2\theta = \\cos^2\theta + sin^2\theta - tan\theta\cos^2\theta$

$\therefore$ The two sides of the equation can't be equal to each other