Question

question 7 (mandatory) (1 point) saved which expression is equivalent to \\( \sin ^{2} \theta+\cos ^{2} \theta+\tan ^{2} \theta \\)? a) \\( \sec ^{2} \theta \\) b) \\( \csc ^{2} \theta \\) c) \\( \tan ^{2} \theta \\) d) \\( \cos ^{2} \theta \\)

Explanation:

Step1: Use Pythagorean identity

We know that \(\sin^{2}\theta+\cos^{2}\theta = 1\). So the given expression \(\sin^{2}\theta+\cos^{2}\theta+\tan^{2}\theta\) becomes \(1+\tan^{2}\theta\).

Step2: Use another trigonometric identity

We also know the identity \(1 + \tan^{2}\theta=\sec^{2}\theta\).

Answer:

A. \(\sec^{2}\theta\)