Question

Prove: ln |tan θ| = ln |sin θ| − ln | cos θ|

Answer 1

Explanation:

We use the law of logarithms that says log A - log B = log (A/B)

ln |sin θ| − ln | cos θ| = ln |sin θ/ cos θ|

We use that the tan A = sin A/cosB

ln |sin θ/ cos θ| = ln |tan θ|

ln |tan θ| = ln |sin θ| − ln | cos θ|

ln |tan θ| = ln |sin θ/ cos θ|

ln |tan θ| = ln |tan θ|