Question

Verify which of the following are identities.

Answer 1

C

Explanation:

Equation 1:

`1+(\cos^(2) \theta)/(\cot^(2) \theta(1-\sin^(2) \theta))\\ \\ 1+(\sin^(2) \theta)/(\cos^(2) \theta) \\ \\ 1+\tan^(2) \theta \\ \\ \sec^(2) \theta`

Equation 2:

`15\cos \theta \left((1)/(\cos \theta)-(\cot \theta)/(\csc \theta) \right) \\ \\ 15\cos \theta \left((1)/(\cos \theta)-(\cos \theta / \sin \theta)/(1/\sin \theta) \right) \\ \\ 15\cos \theta \left((1)/(\cos \theta)-\cos \theta \right) \\ \\ 15\cos \theta \left((1-\cos^(2) \theta)/(\cos \theta) \right) \\ \\ 15(1-\cos^(2) \theta) \\ \\ 15\sin^(2) \theta`