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Proving Trigonometric Identities

Proving Trigonometric Identities. Sec. 5.2a. Prove the algebraic identity. We begin by writing down the left-hand side (LHS), and should e nd by writing the right-hand side (RHS). Each of the e xpressions between should be easily seen to be equivalent to its preceding expression….

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Proving Trigonometric Identities

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  1. Proving Trigonometric Identities Sec. 5.2a

  2. Prove the algebraic identity We begin by writing down the left-hand side (LHS), and should end by writing the right-hand side (RHS). Each of the expressions between should be easily seen to be equivalent to its preceding expression…

  3. General Strategies I 1. The proof begins with the expression on one side of the identity. 2. The proof ends with the expression on the other side. 3. The proof in between consists of showing a sequence of expressions, each one easily seen to be equivalent to its preceding expression. • Since “easily seen” can be a relative phrase, it • is usually safer to err on the side of including too • many steps than too few!!!

  4. Prove the algebraic identity

  5. Prove the algebraic identity

  6. Prove the trigonometric identity

  7. General Strategies II 1. Begin with the more complicated expression and work toward the less complicated expression. 2. If no other move suggests itself, convert the entire expression to one involving sines and cosines. 3. Combine fractions by combining them over a common denominator.

  8. Tell whether or not is an identity: Yes!!! is an identity!!!

  9. Tell whether or not is an identity: This is a phase shift of of the cosine function! …which is the sine function!! Yes!!! is an identity!!!

  10. Combine and Simplify: How can we support this work graphically?

  11. Guided Practice: Prove the given identity.

  12. Guided Practice: Prove the given identity.

  13. Guided Practice: Prove the given identity.

  14. Guided Practice: Prove the given identity.

  15. Guided Practice: Prove the given identity.

  16. Guided Practice: Prove the given identity.

  17. Guided Practice: Prove the given identity.

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