Still have math questions?

Ask our expert tutors
Trigonometry
Question

Consider the derivation of an alternate form of th...

Consider the derivation of an alternate form of the cosine double angle identity. 

1. \( \cos ( 2 x ) = \cos ^ { 2 } ( x ) - \sin ^ { 2 } ( x ) \) 

2. \(= \cos ^ { 2 } ( x ) - ( 1 - \cos ^ { 2 } ( x ) ) \)

3. \(= \cos ^ { 2 } ( x ) - 1 - \cos ^ { 2 } ( x ) \)

4. \(= 2 \cos ^ { 2 } ( x ) - 1\)

What is the error in this derivation? 

In step \( 1 , \cos ( 2 x ) \) is equal to \( \cos ^ { 2 } ( x ) + \sin ^ { 2 } ( x ) \) . 

In step \( 2 , \sin ^ { 2 } ( x ) \) should have been replaced with \( 1 + \) \( \cos ^ { 2 } ( x ) \) . 

In step \( 3 , \cos ^ { 2 } ( x ) - 1 - \cos ^ { 2 } ( x ) \) should be \( \cos ^ { 2 } ( x ) - 1 \) \( + \cos ^ { 2 } ( x ) \) 

In \( \operatorname { step } 4 , 2 \cos ^ { 2 } ( x ) - 1 \) should be \( 1 - 2 \cos ^ { 2 } ( x ) \) 

Answer

option C 

Solution
View full explanation on CameraMath App.