Multiple Angle Formula

Multiple angles formula-trigonometry/double-angle.

Maths Formulas

 Multiple angle formula

The trigonometric functions of multiple angles is the multiple angle formula. Double and triple angles formula are there under the multiple angle formulas. Sine, tangent and cosine are the general functions for the multiple angle formula in Multiple angles formula-trigonometry/double-angle.

Multiple angles formula-trigonometry/double-angle.
trigonometry Multiple angles formula-trigonometry/double-angle.

The sin formula for multiple angle is:Multiple angles formula-trigonometry/double-angle.

sinnθ=k=0ncoskθsinnkθSin[12(nk)]π

Where n=1,2,3,……

General formulas are,

sin2θ=2×cosθsinθ
sin3θ=3sinθ4sin3θ

 The  cosine formula of multiple angle is:Multiple angles formula-trigonometry/double-angle.

Cosnθ=k=0ncoskθsinnkθcos[12(nk)π]

Where n = 1,2,3

The general formula goes as:

cos2θ=cos2θsin2θ
cos3θ=4cos3θ3cosθ

Tangent Multiple Angle formula Multiple angles formula-trigonometry/double-angle.

Tannθ=sinnθcosnθ

Solved Example

Question: Prove that sinx+sin2x1+cosx+cos2x=tanx

Solution:

Using the identities and formulas above we can solve the given identity as shown below:

sinx+sin2x1+cosx+cos2x=tanx

=sinx+2sinxcosx2cos2x+cosx

 Trigonometrical Ratios Multiple Angles Solutions .

Important Trigonometrical Ratios Of Multiple and Sub multiple Angles Multiple angles formula-trigonometry/double-angle.

There are a few important formulas derived in this chapter. In this section, we will go through a few derivations of formulas and other few important formulas used to solve the problem.

Trigonometric multiple angles: sine, cosine, and tangent are general functions for multiple angles. Double angle formula and triple angle formula fall under trigonometric multiple angles. This topic covers derivation for double angle formula and triple angle formula.

Double angle formula: If we put A = B in the trigonometric addition and subtraction formula, then we can easily derive the double angle formula. Formulas for sine, cosine, and tangent are as follows:

  1. sin 2A = 2 sin A cos A

sin 2A = sin A cos A + cos A sin A

= 2 sin A cos A

  1. cos 2A = 2 cosA – s
  2. tan 2A = 2 tan A/ (1- tan2 A)

Triple angle formula: If we put B = 2 A in the trigonometric addition and subtraction formula, then we can derive triple angle formula. Formulas for sine and cosine are as follows:

sin 3A = sin (A + 2A)

= sin A cos 2A + cos A sin 2A

= sin A (1 – 2 sin2A) + 2 (1 – sin2A) s

Trigonometric submultiples angles: Half angle falls under the section of submultiples angles.

Half angle Formula: By replacing the A to A/2 in sine, cosine, and tangent double angle formulas we can derive the half-angle formula. Formulas for sine, cosine, and tangent are as follow:

sin A = 2 sin (A/2) cos (A/2)

Trigonometrical Ratios Of Multiple and Sub multiple Angles

SL Loney Trigonometrical Ratios Of Multiple and Sub multiple Angles consists of 87 questions that are divided into 3 parts:

  • Part 1 of the exercises has 41 solved problems on the topic of multiple angles, double angle, and triple angle. Questions covered in this section are based on finding the value of sine, cosine, and tangent, and proving equations.
  • Part 2 of the exercises has 33 solved problems on the topic of submultiples angle and half-angle. Questions covered in this section are based on finding the cosecant, the cosecant of the half-angle, the cosecant of the supplement of double the angle, finding the values of sine, cosine, and tangent, and proving some equations.
  • Part 3 of exercises has 13 solved problems based on the entire chapter. Questions covered in this section are based on finding trigonometric ratios, trigonometric functions of an angle, and proving few equations.
  • SL Loney Plane Trigonometry Solutions for Trigonometrical Ratios Multiple and Sub multiple Angles are easily available that are free of cost for all students aspiring to give JEE.
  • SL Loney Solutions are the most trustworthy source of study material for topics like trigonometry that is one of the core topics of maths for Class 12 and has a significance in JEE for maths.
  • The solutions designed by our team are specially designed to help you gain better math fluency and solve the complex and tricky questions efficiently.
  • Instasolve provides accurate solutions with easy solving and formula application techniques for SL Loney Plane Trigonometry.
Summary
Multiple angle formula - trigonometry .
Article Name
Multiple angle formula - trigonometry .
Description
The trigonometric functions of multiple angles is the multiple angle formula. Double and triple angles formula are there under the multiple angle formulas. Sine, tangent and cosine are the general functions for the multiple angle formula.
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