5 wonderful tricks to solve ques related to trigonometric identities proofing.
Answers
Step-by-step explanation:
Tip 1) Always Start from the More Complex Side
To prove a trigonometric identity, we always start from either the left hand side (LHS) or the right hand side (RHS) and apply the identities step by step until we reach the other side. However, smart students always start from the more complex side. This is because it is a lot easier to eliminate terms to make a complex function simple than to find ways to introduce terms to make a simple function complex.
Example Q1) Prove the identity tan⁴x = sec²x (tan²x-1)+1
Approach: It would be wise to start proving this from the right hand side (RHS) since it is more complex.
Tip 2) Express everything into Sine and Cosine
To both sides of the equation, express all tan , cosec , sec and cot in terms of sin and cos . This is to standardize both sides of the trigonometric identity such that it is easier to compare one side to another.
Tip 3) Combine Terms into a Single Fraction
When there are 2 terms on one side and 1 term on the other side, combine the side with 2 terms into 1 fraction after making their denominators the same.
Tip 4) Use Pythagorean Identities to transform between sin²x and cos²x
Pay special attention to addition of squared trigonometry terms. Apply the Pythagorean identities when necessary. Especially sin²x+cos²x=1 since all the other trigo terms have been converted into sine and cosine. This identity can be used to convert into and vice versa. It can also be used to remove both by turning it into 1.
Tip 5) Know when to Apply Double Angle Formula (DAF)
Observe every trigonometric term in the question. Are there terms with angles that are 2 times of another? If there are, be ready to use DAF to transform them into the same angle. For example, if you see sinθ and cot(θ/2) in the same question, you have to use DAF since θ is 2 times of (θ/2).
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Step-by-step explanation:
Tip 1) Always Start from the More Complex Side
Tip 2) Express everything into Sine and Cosine
Tip 3) Combine Terms into a Single Fraction
Tip 4) Use Pythagorean Identities to transform between sin²x and cos²x
Tip 5) Know when to Apply Double Angle Formula (DAF)
Tip 6) Know when to Apply Addition Formula (AF)
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