Consider the following:1. 2. 3. Which of the above are identities?

1 and 3 ONLY. Statement 1: and , so it is true. Statement 2: , so it is false. Statement 3: , so it is true. Only 1 and 3 are correct.

Consider the following: 1. \sin^{4}\theta-\sin^{2}\theta=\cos^{4}\theta-\cos^{2}\theta 2. \sin^{4}\theta+\cos^{4}\theta=1+2\sin^{2}\theta\cos^{2}\theta 3. \tan^{4}\theta+\tan^{2}\theta=\sec^{4}\theta-\sec^{2}\theta Which of the above are identities?

A. 1 and 2 ONLY
B. 2 and 3 ONLY
C. 1 and 3 ONLY ✓
D. 1, 2 and 3

Correct Answer: C. 1 and 3 ONLY

Explanation

Statement 1: \sin^2\theta(\sin^2\theta - 1) = -\sin^2\theta\cos^2\theta and \cos^2\theta(\cos^2\theta - 1) = -\sin^2\theta\cos^2\theta, so it is true. Statement 2: (\sin^2\theta+\cos^2\theta)^2 = 1 \implies \sin^4\theta + \cos^4\theta = 1 - 2\sin^2\theta\cos^2\theta, so it is false. Statement 3: \tan^2\theta(\tan^2\theta+1) = \tan^2\theta\sec^2\theta = (\sec^2\theta-1)\sec^2\theta = \sec^4\theta - \sec^2\theta, so it is true. Only 1 and 3 are correct.

Consider the following:<br><br>1. \sin^{4}\theta-\sin^{2}\theta=\cos^{4}\theta-\cos^{2}\theta<br>2. \sin^{4}\theta+\cos^{4}\theta=1+2\sin^{2}\theta\cos^{2}\theta<br>3. \tan^{4}\theta+\tan^{2}\theta=\sec^{4}\theta-\sec^{2}\theta<br><br>Which of the above are identities?

Explanation

Related questions on Trigonometry