Further Trigonometry Identity (Proving question)

In summary, to prove the equation (sin3A-sinA)/(cosA+cos3A)=tanA, we can use the identities sin(x) - sin(y) = 2cos((x+y)/2)sin((x-y/2) and cos(x) + cos(y) = 2cos((x+y)/2)cos((x-y)/2) to simplify the expression. By expanding and rearranging, we can show that both sides are equal, proving the given equation.
  • #1
wei1006
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1) Question:
Show that (sin3A-sinA)/(cosA+cos3A)=tanA

2) Relevant equations:
tan A=sinA/cos A
1+tan^2A=sec^A
cot A=1/tanA
cot A=cos A/sinA
sin^2A+cos^2A=1
secA=1/cos A
cosecA=1/sinA
1+cosec^2A= cot^2A
sin2A=2sinAcosA
cos2A=1-2sin^2A=cos^2A-sin^2A=2cos^A-1
tan2A=(2tanA)/1-tan^2A

3)Attempt:
(sin3A-sinA)/(cos A+cos3A)
=(2sin3/2Acos3/2A)-(sinAcosA)/(cos^2(1/2)A-sin^2(1/2)A)+(cos^2(3/2)A-sin^2(3/2)A)
I tried expanding but ended up confusing myself...
 
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  • #2

FAQ: Further Trigonometry Identity (Proving question)

1. What is trigonometry identity?

Trigonometry identity is a mathematical equation that shows the relationship between different trigonometric functions. It is used to prove or simplify other trigonometric equations.

2. What is the purpose of proving trigonometry identity?

The purpose of proving trigonometry identity is to establish the validity of a given equation or to simplify a more complex equation into a simpler form. It is an important tool in solving trigonometric problems.

3. How do you prove trigonometry identity?

To prove trigonometry identity, you need to use basic trigonometric identities like Pythagorean identities, quotient identities, and reciprocal identities. You can also use algebraic manipulation and substitution to simplify the equation and show that both sides are equivalent.

4. Can all trigonometric equations be proven using trigonometry identity?

No, not all trigonometric equations can be proven using trigonometry identity. Some equations may require other mathematical concepts or techniques to be proven.

5. What are some common trigonometry identities?

Some common trigonometry identities include the Pythagorean identities (sin^2x + cos^2x = 1), quotient identities (tanx = sinx/cosx), and reciprocal identities (cscx = 1/sinx). There are also double angle, half angle, and sum/difference identities that are commonly used in proving trigonometric equations.

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