Starting with the identity $\sin ^ { 2 } x + \cos ^ { 2 } x = 1$ , choose the right trigonometric identity.
A) $\sec ^ { 2 } x = 1 + \tan ^ { 2 } x$
B) $\sec ^ { 2 } x = 1 - \tan ^ { 2 } x$
C) $\cot ^ { 2 } x = 1 - \tan ^ { 2 } x$
D) $\sin ^ { 2 } x = 1 + \tan ^ { 2 } x$
E) $\sec ^ { 2 } x = 1 + \csc ^ { 2 } x$

Question

Starting with the identity $\sin ^ { 2 } x + \cos ^ { 2 } x = 1$ , choose the right trigonometric identity. 
A) $\sec ^ { 2 } x = 1 + \tan ^ { 2 } x$
B) $\sec ^ { 2 } x = 1 - \tan ^ { 2 } x$
C) $\cot ^ { 2 } x = 1 - \tan ^ { 2 } x$
D) $\sin ^ { 2 } x = 1 + \tan ^ { 2 } x$
E) $\sec ^ { 2 } x = 1 + \csc ^ { 2 } x$

Quizplus · Accepted Answer

Dividing the identity $\sin^2x + \cos^2x = 1$ by $\cos^2x$ gives $\tan^2x + 1 = \sec^2x$, which matches choice A.

Starting with the Identity sin⁡2x+cos⁡2x=1\sin ^ { 2 } x + \cos ^ { 2 } x = 1sin2x+cos2x=1

Starting with the Identity $\sin ^ { 2 } x + \cos ^ { 2 } x = 1$