Trigonometry proof of identity is a common type of question included in O Level’s complementary mathematics curriculum. When the word ‘triangle’ came out, even high school students would break out into a cold sweat. This is because, unlike most of the Math topics, there is no standard plug-and-play approach to trigonometry problems. Each question is a new puzzle in which students must find a path from start to finish. Very often, students approach these problems by observing one step at a time.
Even though every problem of trigonometry is unique in its own way, there is usually a “rule of thumb” for learners to follow, so that they do not become misled. Here, we reveal some cool tips to help students conquer trigonometry with the aid of trigonometry tutoring help.
#1 Start Solving from Complex Side
To prove trigonometric identities, we always start from the left (LHS) or right (RHS) and step through the identities until we reach the opposite side. But smart learners always start from the difficult side. They know that it’s much easier to rule out a term to make a complex function simple than it is to find a way to introduce a term to make a simple function complex.
#2 Convert everything into Sine and Cosine (if possible)
Express all tan, cosec, sec, and cot as sin and cos for both sides of the equation. This is to standardize both sides of the trigonometric identities, making it easier to compare one side to the other.
#3 Use Pythagoras Theorem basics to evaluate between sin²x and cos²x
Pay special attention to adding squares in trigonometry. Apply the Pythagorean formula if necessary. Specifically, sin²x + cos²x = 1. This is because all other trigonometric terms have been converted to sines and cosines. You can use this identifier to convert and vice versa. You can also use it to remove both by replacing it with 1.
#4 Apply Double Angle Formula (when needed)
Pay attention to each trigonometric term in question. Is there a variable whose angle is twice that of another variable? If so, be prepared to use a DAF to convert to the same angle. For example, if sinθ and cot(θ/2) come up in the same question, then θ is doubled (θ/2), so you should use DAF.
#5 Apply the Expand| Factorize| Simplify| Cancelling Method
A lot of students have the strong belief that every single problem to prove trigonometry requires the utilization of trigonometric identities in the formula table. Whenever they get stuck, it’s not uncommon for them to stare blankly at the official sheet and pray that the answer will magically “jump out”. This is because most confirmatory questions revolve around good old-fashioned extensions, factorizations, simplifications, and abolitions of similar terms. In fact, some exam questions do not even require the student to use the rules of trigonometry.
#6 Take one step at a time
Proof of trigonometric functions is an art. There are several ways to find the answer. Naturally, some methods are more elegant and concise, while others are crude, voluminous, and ugly. But no matter which route you choose; you will get a quote as long as you can get to your final destination.
After solving many exam questions, some students tend to robot proving LHS = RHS whenever they see an equation involving a trigonometric function. Even when faced with the question “Solve the trigonometric equation…”… always read the question carefully!
With the help of these cool tips and Trigonometry Tutoring Help, you are now ready to prove LHS = RHS!