Answer to Question #86085 in Trigonometry for Ice Prinxxx

Question

If cosΦ = C, express in terms of C tan² Φ + 2 cos Φ

Answer 1

Solution:

$$\tan^2\Phi+2\cos\Phi=\frac{\sin^2\Phi} {\cos^2\Phi} +2\cos\Phi=\frac{1-\cos^2\Phi} {\cos^2\Phi} +2\cos\Phi$$

Let's take into account that $\cos\Phi=C:$

$$\frac{1-\cos^2\Phi} {\cos^2\Phi} +2\cos\Phi=\frac{1-C^2} {C^2} +2C=\frac{1} {C^2}+2C-1$$

Answer:

$$\frac{1} {C^2}+2C-1$$