Trigonometric Identities

    Algebraic formulas along with the trigonometric definitions and the Pythagorean Identities can produce quite a number of trigonometric identities.  A beginning strategy for proving a trigonometric identity is to reduce the more complicated side of the equation to the simpler side. If no simplification is obvious, then perhaps express every trigonometric function on the more complicated side of the equation in terms of sines and cosines, and then reduce this expression to the simpler side.

Definition (Trigonometric Identity) A trigonometric equation that becomes true when the variable is replaced by every permissible number is called a trigonometric identity.

    In this topic we verify the following trigonometric identities:

        (1)

        (2)

        (3)

        (4)

        (5)

        (6)

        (7)

        (8)

        (9)

        (10)

Example (Trigonometric Identities) Verify the trigonometric identitiy

     Solution. We verify the identities by transforming the left hand side into the right hand side.
     












Example (Trigonometric Identities) Verify the trigonometric identitiy

     Solution. We verify the identities by transforming the left hand side into the right hand side.
     











Example (Trigonometric Identities) Verify the trigonometric identitiy

     Solution. We verify the identities by transforming the left hand side into the right hand side.
     











Example (Trigonometric Identities) Verify the trigonometric identitiy

     Solution. We verify the identities by transforming the left hand side into the right hand side.
     













Example (Trigonometric Identities) Verify the trigonometric identitiy

     Solution. We verify the identities by transforming the left hand side into the right hand side.
     











Example (Trigonometric Identities) Verify the trigonometric identitiy

     Solution. We verify the identities by transforming the left hand side into the right hand side.
     













Example (Trigonometric Identities) Verify the trigonometric identitiy

     Solution. We verify the identities by transforming the left hand side into the right hand side.
     













Example (Trigonometric Identities) Verify the trigonometric identitiy

     Solution. We verify the identities by transforming the left hand side into the right hand side.
     











Example (Trigonometric Identities) Verify the trigonometric identitiy

     Solution. We verify the identities by transforming the left hand side into the right hand side.
     















Example (Trigonometric Identities) Verify the trigonometric identitiy

     Solution. We verify the identities by transforming the left hand side into the right hand side.
     

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Cite this as:
Trigonometric Identities
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/trigonometric-identities.html