Question

Which of the following are identities? Check all that apply.

Answer 1

Answer:

Option B and Option D.

Step-by-step explanation:

Among the options, only B and D represent identities, they are known has pythagorean identities because they are obtained form a right triangle and its trigonometry.

All pythagorean identities are

$sin^{2}\alpha+cos^{2} \alpha =1$

$tan^{2}\alpha +1=sec^{2}\alpha$

$cot^{2} \alpha +1=csc^{2} \alpha$

If you compare only B and D represent two of these identities.

Option A and C don't represent identities because they are written wrong, if you compare with all three identities above, you will realize this.

Therefore, the right options are B and D.

Answer 2

Answer: Option 'B' and 'D' are correct.

Step-by-step explanation:

Since we know the trigonometric identities as follows :

$\sin^2x+\cos^2 x=1\\\\\sec^2 x-\tan^2 x=1\\\\cosec^2 x-\cot^2 x=1$

According to options , we get that

$cosec^2 x=1+\cot^2 x$ satisfies the identities.

and $\sin^2x+\cos^2 x=1$ is the identity.

Hence, Option 'B' and 'D' are correct.