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).

Card 1 of 1 free previews

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).

More in Maths

📐

Squares of Numbers from 1 to 50 — Complete Table, Tricks & Examples

Squares of numbers from 1 to 50 — complete table from 1² = 1 to 50² = 2500. Learn square values, shortcut tricks, patterns, perfect squares & solved examples.

📐

Successive Discount Formula and Examples

Learn the exact formula for calculating successive discounts. Understand why two 10% discounts are NOT equal to a single 20% discount with examples.

📐

Successor of 10378695 — Answer and Explanation

The successor of 10378695 is 10378696. The predecessor is 10378694. Learn what successor and predecessor mean with examples.

📐

What is the Sum of an Infinite Geometric Progression (GP)?

Sum of infinite GP: S∞ = a/(1−r), valid when |r| < 1. a = first term, r = common ratio. Examples like 1+1/2+1/4+...= 2.

📐

Surface Area and Volume Formulas for Class 10 (All Shapes)

All surface area and volume formulas for Class 10: Cube, Cuboid, Cylinder, Cone, Sphere, Hemisphere, Frustum. TSA, CSA, and Volume included.

Study Smarter with Shinyu.ai

Turn this guide into revision flashcards, a practice exam, or an AI-generated podcast — free, no signup required.