What are the steps in proving trigonometric identities?
STEP 1: Convert all sec, csc, cot, and tan to sin and cos. Most of this can be done using the quotient and reciprocal identities. STEP 2: Check all the angles for sums and differences and use the appropriate identities to remove them. STEP 3: Check for angle multiples and remove them using the appropriate formulas.
How do you prove trigonometric identities Questions?
Proving the problems on trigonometric identities:
- ( 1 – sin A)/(1 + sin A) = (sec A – tan A)2 Solution: L.H.S = (1 – sin A)/(1 + sin A)
- Prove that, √{(sec θ – 1)/(sec θ + 1)} = cosec θ – cot θ. Solution: L.H.S.= √{(sec θ – 1)/(sec θ + 1)}
- tan4 θ + tan2 θ = sec4 θ – sec2 θ
What is one important consideration when proving trigonometric identities?
Work on the most complex side and simplify it so that it has the same form as the simplest side. Don’t assume the identity to prove the identity. This means don’t work on both sides of the equals side and try to meet in the middle.
How do you prove identities?
There are only three ways to prove an identity: left to right, right to left, or meet in the middle. Never prove an identity by simplifying both sides simultaneously.
What are the fundamental trigonometric identities?
Since, cos (− θ ) = cos θ , cos (− θ ) = cos θ , cosine is an even function….Verifying the Fundamental Trigonometric Identities.
| Quotient Identities | |
|---|---|
| tan θ = sin θ cos θ tan θ = sin θ cos θ | cot θ = cos θ sin θ cot θ = cos θ sin θ |
What is the easiest way to learn trigonometry chapters?
7 Easy Steps to Learn Trigonometry
- Study all the basics of trigonometric angles.
- Study right-angle triangle concepts.
- Pythagoras theorem.
- Sine rule and Cosine rule.
- List all the important identities of trigonometry.
- Remember the trigonometry table.
- Be thorough with the trigonometric formulas.
What are the 3 trigonometric identities?
Sine, cosine and tangent are the primary trigonometry functions whereas cotangent, secant and cosecant are the other three functions….The reciprocal trigonometric identities are:
- Sin θ = 1/Csc θ or Csc θ = 1/Sin θ
- Cos θ = 1/Sec θ or Sec θ = 1/Cos θ
- Tan θ = 1/Cot θ or Cot θ = 1/Tan θ