Equality
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
sec θ - sinθ tanθ = cos θ
prove the identity = ?
Step 02:
We must use the trigonometric identities to find the solution.
sec θ - sinθ tanθ = cos θ
[tex]\frac{1}{\cos\text{ }\theta}-\sin \theta\cdot\frac{\sin\text{ }\theta}{\text{cos}\theta}=\cos \text{ }\theta[/tex][tex]\frac{1}{\cos\theta}-\frac{\sin^2\theta}{\cos\theta}=\cos \theta[/tex][tex]\frac{1-\sin^2\theta}{\cos\theta}=\cos \theta[/tex][tex]\frac{\cos^2\theta}{\cos\theta}=\cos \theta[/tex][tex]\cos \text{ }\theta\text{ = cos }\theta[/tex]The answer is:
Equality is verified.
cos θ = cos θ