Krushnaraj Pandya said:Homework Statement
Show that sec(x-(pi/2))+tan(x-(pi/2))=tan((x/2)+pi/12))
The Attempt at a Solution
I applied all sorts of half angle formulas to convert it in terms of tan, I got LHS as (tan((x/2)-(pi/6))+1)^2/1-tan^2(x/2-(pi/6)) but I'm sure there must be a simple easy method to get the RHS (PS this is part of a bigger problem, I got the answer as LHS, I need to equate it to RHS for my answer to be correct
right, got it. I'll need to post the entire question thenRay Vickson said:If you plot both sides you will see that the equation you wrote is not correct.
Here is a piece of advice: always try plotting first, before attempting to prove an unfamiliar result; sometimes you can save yourself hours of useless work by doing that.
Simple trigonometric simplification is a process of reducing complex trigonometric expressions into simpler forms using trigonometric identities and basic algebraic techniques.
Simple trigonometric simplification is important because it allows us to solve complex trigonometric equations and expressions more easily and accurately. It also helps in understanding the relationships between different trigonometric functions.
Some common trigonometric identities used in simplification are the Pythagorean identities, double angle identities, half angle identities, and sum and difference identities.
To simplify a trigonometric expression, you can follow these steps:
1. Use the given identities to replace any complex trigonometric functions with simpler ones.
2. Apply basic algebraic techniques such as factoring, combining like terms, and using the distributive property.
3. Simplify the expression further by using identities again if needed.
4. Check your final answer by plugging in values for the variables or using a calculator.
Yes, some common mistakes to avoid when simplifying trigonometric expressions include:
- Forgetting to use parentheses when applying distributive property.
- Not simplifying fractions or rational expressions.
- Mixing up the signs of trigonometric functions (e.g. using cosine instead of sine).
It is important to double check your work and be careful with signs and operations when simplifying trigonometric expressions.