Question

TanA - secA =

1. sinA-1/cosA
2. sin^2A-cosA
3. cos^2A-1/cosA

Please explain, don’t bother answering if you’re not going to explain. Ty!

Answer 1

The answer is 2. sin2A-cosA. This can be seen by using the trigonometric identities sin2A=2sinAcosA and cos2A=cos2A-sin2A. The expression tanA-secA can then be simplified to sinA/cosA-1/cosA, which can be further simplified to (2sinAcosA-cos2A)/cosA, which can be further simplified to 2sinAcosA-cosA, which can finally be simplified to sin2A-cosA.