Question

I do not understand this problem very well and I would like to know if you could help me. :"/prove the identity (step and reason)

Answer 1

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

`\frac{1}{\cos\text{ }\theta}-\sin \theta\cdot\frac{\sin\text{ }\theta}{\text{cos}\theta}=\cos \text{ }\theta`
`(1)/(\cos\theta)-(\sin^2\theta)/(\cos\theta)=\cos \theta`
`(1-\sin^2\theta)/(\cos\theta)=\cos \theta`
`(\cos^2\theta)/(\cos\theta)=\cos \theta`
`\cos \text{ }\theta\text{ = cos }\theta`

The answer is:

Equality is verified.

cos θ = cos θ