Negative angle identities -Trigonometry formulas

Negative angle identities 1. sin(−t)=−sin(t) 2. cos(−t)=cos(t) 3. tan(−t)=−tan(t) 4. cot(−t)=−cot(t) 5. sec(−t)=sec(t) 6. cosec(−t)=−cosec(t) Example 1: What is \(\cos \left(-\frac {3\pi }{4}\right) \)? Solution: cos-3π4=cos3π4=-22 Example 2: What is \(\sin \left(-\frac {\pi }{2}\right) \)? Solution:…

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Product-to-Sum Identities

Product-to-Sum Identities 1. sinα·sinβ=12cos(α–β)–cos(α+β) 2. cosα·cosβ=12cos(α–β)+cos(α+β) 3. sinα·cosβ=12sin(α+β)+sin(α–β) 4. cosα·sinβ=12sin(α+β)–sin(α–β) 5. tanα·tanβ=(tanα+tanβ)(cotα+cotβ) 6. cotα·cotβ=(cotα+cotβ)(tanα+tanβ) 7. tanα·cotβ=(tanα+cotβ)(cotα+tanβ) Example: Write cos 3x cos 2x as a sum Solution: cosα·cosβ=12[cos(α–β)+cos(α+β)] cos3x·cos2x=12[cos(3x–2x)+cos(3x+2x)] cos3x·cos2x=12[cosx+cos5x] cos3x·cos2x=cosx2+cos5x2

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