107k views
0 votes
Verify sin^4x-sin^2x=cos^4x-cos^2x is an identity

User Gaby Solis
by
7.8k points

1 Answer

4 votes

ANSWER

See below

Step-by-step explanation

We want to verify that,


{ \sin ^(4) x} - { \sin^(2) x} = { \cos ^(4) x} - { \cos^(2) x}

To verify this identity, we can take the left hand side simplify it to get the right hand side or vice versa.


{ \sin ^(4) x} - { \sin^(2) x} =( { \sin ^(2) x} )^(2) - { \sin^(2) x}


{ \sin ^(4) x} - { \sin^(2) x} ={ \sin ^(2) x}({ \sin ^(2) x} - 1)


{ \sin ^(4) x} - { \sin^(2) x} ={ \sin ^(2) x} * - (1 - { \sin ^(2) x})


{ \sin ^(4) x} - { \sin^(2) x} =({1 - \cos^(2) x} )* - ({ \cos^(2) x})


{ \sin ^(4) x} - { \sin^(2) x} =({ \cos^(2) x} - 1 )* ({ \cos^(2) x})

We now expand the right hand side to get:


{ \sin ^(4) x} - { \sin^(2) x} = { \cos ^(4) x} - { \cos^(2) x}

User Hemi
by
8.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories