114F08PSTrigIds - Math 114 Special Problem Session I:...

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Unformatted text preview: Math 114 Special Problem Session I: Verifying Trigonometric Identities Fall, 2008 State the following basic identities: Pythagorean, Quotient, Reciprocal, Cofunction, Even/Odd Verify the following identities. Work on ONE side ONLY. Write going DOWN: sec θ sin θ = tan θ 1. 2. 1 + cot 2 ( − θ ) = csc 2 θ 3. π sin θ ( cot θ + tan θ ) = csc − θ 2 sin θ 1 + cos θ 4. π sec( − θ ) cos − θ = sec θ sin θ 2 csc θ − cot θ = 5. 6. 1 − 2 cos 2 θ = tan θ − cot θ sin θ cos θ 7. csc θ − 1 = csc θ + 1 1 − sin θ 1 + sin θ 1− 8. sin 2 θ = − cos θ 1 − cos θ 9. 1 − cot 2 θ 1 + cot 2 θ + 2 cos 2 θ = 1 10. csc θ − 1 cot θ = cot θ csc θ + 1 11. sec 2 θ − tan 2 θ + tan θ = sin θ + cos θ sec θ 12. 1 − cos θ 2 = ( csc θ − cot θ ) 1 + cos θ 13. 1 + sin θ cos θ + 1 + sin θ cos θ = 2 sec θ ( sec θ 14. − tan θ ) + 1 = 2 tan θ csc θ ( sec θ − tan θ ) 2 1 ...
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