Determine if the following is an identity.
-$$1 + \sec ^ { 2 } x \sin ^ { 2 } x = \sec ^ { 2 } x$$
A) Identity
B) Not an identity

Question

Quizplus · Accepted Answer

Using the identity $ \sec ^ { 2 } x = 1 + \tan ^ { 2 } x $ and $ \sin ^ { 2 } x = \frac { \tan ^ { 2 } x } { 1 + \tan ^ { 2 } x } $, we have$$1 + \sec ^ { 2 } x \sin ^ { 2 } x = 1 + ( 1 + \tan ^ { 2 } x ) \left( \frac { \tan ^ { 2 } x } { 1 + \tan ^ { 2 } x } \right)$$$$= 1 + \tan ^ { 2 } x = \sec ^ { 2 } x$$

Determine If the Following Is an Identity 1+sec⁡2xsin⁡2x=sec⁡2x1 + \sec ^ { 2 } x \sin ^ { 2 } x = \sec ^ { 2 } x1+sec2xsin2x=sec2x

Determine If the Following Is an Identity $1 + \sec ^ { 2 } x \sin ^ { 2 } x = \sec ^ { 2 } x$