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Here is a comprehensive list of important trigonometric formulas involving sine and cosine, presented in a copy-friendly format:

Sum and Difference Formulas

Difference of Sines and Cosines

Product-to-Sum Formulas

Fundamental Trigonometric Identities

Sine and Cosine of Complementary Angles

Double Angle Formulas

Sum and Difference Formulas for Sine and Cosine

These formulas are essential for solving trigonometric equations, simplifying expressions, and working on problems involving periodic behavior in calculus and physics.

Here is a comprehensive list of important trigonometric formulas involving sine and cosine, presented in a copy-friendly format:

Sum and Difference Formulas

Difference of Sines and Cosines

Product-to-Sum Formulas

Fundamental Trigonometric Identities

Sine and Cosine of Complementary Angles

Double Angle Formulas

Sum and Difference Formulas for Sine and Cosine

These formulas are essential for 

• sin²θ + cos²θ = 1.
• tan²θ + 1 = sec²θ
• cot²θ + 1 = cosec²θ
• sin 2θ = 2 sin θ cos θ
• cos 2θ = cos²θ – sin²θ
• tan 2θ = 2 tan θ / (1 – tan²θ)
• cot 2θ = (cot²θ – 1) / 2 cot θ

• Here’s a full list of important trigonometric formulas involving sine and cosine:

  Sum and Difference Formulas

  1. Sum of Sine and Cosine:

  
     \sin(x) + \cos(x) = \sqrt{2} \cdot \sin\left(x + \frac{\pi}{4}\right)
  

  
     \sin(x) + \cos(x) = \sqrt{2} \cdot \cos\left(x - \frac{\pi}{4}\right)
  

  2. Sum of Sines:

  
     \sin(A) + \sin(B) = 2 \cdot \sin\left(\frac{A + B}{2}\right) \cdot \cos\left(\frac{A - B}{2}\right)
  

  3. Sum of Cosines:

  
     \cos(A) + \cos(B) = 2 \cdot \cos\left(\frac{A + B}{2}\right) \cdot \cos\left(\frac{A - B}{2}\right)
  

  Difference of Sines and Cosines

  4. Difference of Sines:

  
     \sin(A) - \sin(B) = 2 \cdot \cos\left(\frac{A + B}{2}\right) \cdot \sin\left(\frac{A - B}{2}\right)
  

  5. Difference of Cosines:

  
     \cos(A) - \cos(B) = -2 \cdot \sin\left(\frac{A + B}{2}\right) \cdot \sin\left(\frac{A - B}{2}\right)
  

  Product-to-Sum Formulas

  6. Product of Sines:

  
     \sin(A) \cdot \sin(B) = \frac{1}{2} \left[\cos(A - B) - \cos(A + B)\right]
  

  7. Product of Cosines:

  
     \cos(A) \cdot \cos(B) = \frac{1}{2} \left[\cos(A - B) + \cos(A + B)\right]
  

  8. Product of Sine and Cosine:

  
     \sin(A) \cdot \cos(B) = \frac{1}{2} \left[\sin(A + B) + \sin(A - B)\right]
  

  Fundamental Trigonometric Identities

  9. Pythagorean Identity:

  
     \sin^2(x) + \cos^2(x) = 1
  

  10. Sine and Cosine of Complementary Angles:

  
     \sin\left(\frac{\pi}{2} - x\right) = \cos(x)
     \quad \text{and} \quad
     \cos\left(\frac{\pi}{2} - x\right) = \sin(x)
  

  Double Angle Formulas

  11. Double Angle for Sine:

  
     \sin(2x) = 2 \sin(x) \cos(x)
  

  12. Double Angle for Cosine:

  
     \cos(2x) = \cos^2(x) - \sin^2(x) = 2\cos^2(x) - 1 = 1 - 2\sin^2(x)
  

  Sum and Difference Formulas for Sine and Cosine

  13. Sum of Angles:

  
     \sin(A + B) = \sin(A)\cos(B) + \cos(A)\sin(B)
  

  \cos(A + B) = \cos(A)\cos(B) - \sin(A)\sin(B) ]

  14. Difference of Angles:

  
     \sin(A - B) = \sin(A)\cos(B) - \cos(A)\sin(B)
  

  \cos(A - B) = \cos(A)\cos(B) + \sin(A)\sin(B) ]

  These formulas are essential for solving trigonometric equations, simplifying expressions, and working in calculus or physics problems involving waves or periodic behavior.

• The "sino + coso" formulas likely refer to trigonometric identities that involve combinations of the sine and cosine functions. There are a few important formulas and identities in trigonometry involving sine (sin) and cosine (cos). Here are the key ones:

1. Sum of Sine and Cosine

This identity combines sine and cosine into one expression:

\sin(x) + \cos(x) = \sqrt{2} \cdot \sin\left(x + \frac{\pi}{4}\right)

\sin(x) + \cos(x) = \sqrt{2} \cdot \cos\left(x - \frac{\pi}{4}\right)

These formulas show that a sum of sine and cosine can be rewritten as a single trigonometric function with a phase shift.

2. Sum of Sines

For the sum of two sine functions, the identity is:

\sin(A) + \sin(B) = 2 \cdot \sin\left(\frac{A + B}{2}\right) \cdot \cos\left(\frac{A - B}{2}\right)

3. Sum of Cosines

For the sum of two cosine functions, the identity is:

\cos(A) + \cos(B) = 2 \cdot \cos\left(\frac{A + B}{2}\right) \cdot \cos\left(\frac{A - B}{2}\right)

4. Product-to-Sum Formulas

These formulas are useful when working with products of sine and cosine functions:

\sin(A) \cdot \sin(B) = \frac{1}{2} \left[\cos(A - B) - \cos(A + B)\right]

\cos(A) \cdot \cos(B) = \frac{1}{2} \left[\cos(A - B) + \cos(A + B)\right] ]

\sin(A) \cdot \cos(B) = \frac{1}{2} \left[\sin(A + B) + \sin(A - B)\right]

5. Pythagorean Identity

The most famous identity involving sine and cosine is the Pythagorean identity:

\sin^2(x) + \cos^2(x) = 1

This identity is fundamental to many trigonometric simplifications.

Summary

The sum and product of sine and cosine functions can be simplified using these identities to create more manageable expressions, especially in calculus or physics problems involving waves or oscillations.

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