Question

Write the trigonometric expression in terms of sine and cosine, and then simplify. cos theta - sec theta / sin theta

Answer 1

What you wrote is ambiguous. Did you mean \(\cos \theta - \dfrac{\sec \theta}{\sin \theta}\) or \(\dfrac{\cos \theta - \sec \theta}{\sin \theta}\)?

Answer 2

The second figure

Answer 3

Taken directly off webassign homework. Spent two hours fiddling with it

Answer 4

Well, \(\sec \theta = \dfrac{1}{\cos \theta}\), so:\[\dfrac{\cos \theta - \color{red}{\sec \theta}}{\sin \theta}=\dfrac{\cos \theta - \color{red}{\dfrac{1}{\cos \theta}}}{\sin \theta}=\frac{\left( \dfrac{\cos^2 \theta - 1}{\cos \theta}\right)}{\sin \theta}=\dfrac{\color{blue}{\cos^2 \theta - 1}}{\sin \theta \cos \theta}\]You can simplify the blue bit using the Pythagorean identity \(\sin^2 \theta + \cos^2 \theta = 1\), which lets everything simplify further.

Answer 5

Thanks sooo much. That cos^2-1 threw me off the track for sure. -sin^2 theta. Then simplified it down to -tan(theta). Again thanks so much! I'll be back to learn how the equation input process works on this site. For now back to verifying identities! Yeah