Study Guides/Maths/Trigonometry Formulas: Sin C + Sin D and Sin 3 Theta
Study Guide · Maths

Formulas for Sin C + Sin D and Sin 3θ

In Class 11 Mathematics, the 'Trigonometric Functions' chapter introduces many new identities. The 'Sum to Product' formulas (often called the C & D formulas) and the 'Multiple Angle' formulas are the most heavily used in calculus and algebra.

Question (Click to Flip)

What is the formula of Sin C + Sin D?

Answer

The formula is: Sin C + Sin D = 2 Sin((C+D)/2) Cos((C-D)/2).

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Key Facts

Sin C + Sin D: Used to convert Addition into Multiplication.

Sin 3θ: $3\sin\theta - 4\sin^3\theta$.

1. The Sin C + Sin D Formulas

These formulas are used to convert the sum or difference of two sine/cosine functions into a multiplication (product) format.

  • $\sin C + \sin D = 2 \sin(\frac{C+D}{2}) \cos(\frac{C-D}{2})$
  • $\sin C - \sin D = 2 \cos(\frac{C+D}{2}) \sin(\frac{C-D}{2})$
  • $\cos C + \cos D = 2 \cos(\frac{C+D}{2}) \cos(\frac{C-D}{2})$
  • $\cos C - \cos D = -2 \sin(\frac{C+D}{2}) \sin(\frac{C-D}{2})$ (Note the negative sign in the last formula!)

2. The Sin 3θ Formula

This is a multiple-angle identity used to break down an angle that is multiplied by 3 into single angles.

  • Formula: $\sin(3\theta) = 3\sin\theta - 4\sin^3\theta$

(Trick to remember: Think of the number 34. The 3 comes first, then the 4 with the cube!)

  • Similarly, the formula for Cos 3θ is the reverse: $\cos(3\theta) = 4\cos^3\theta - 3\cos\theta$.

Questions and Answers

What is the formula of Sin C + Sin D?+

The formula is: Sin C + Sin D = 2 Sin((C+D)/2) Cos((C-D)/2).

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