Question

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

Answer 1

Option B and Option D.

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.

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.