Question

Verify which of the following are identities.

Answer 1

the person above me is right :)

Explanation:

Answer 2

Only the second equation is an identity

Explanation:

1)

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

This one is not an identity.

2)

`19\cos \theta\left( (1)/(\cos \theta)-(\tan \theta)/(\csc \theta) \right)= \\\\\\19\cos \theta \left( (1)/(\cos \theta)-(\sin^2 \theta)/(\cos \theta) \right)= \\\\\\19\cos \theta \left( (1-\sin^2 \theta)/(\cos \theta)\right)= \\\\\\19\cos \theta \left( (\cos^2 \theta)/(\cos \theta)\right)= \\\\\\19\cos \theta (\cos \theta)= \\\\\\19\cos^2 \theta = 19\cos^2 \theta`

This one is an identity. Therefore, only the second equation is an identity. Hope this helps!