- #1
Alex1067
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Homework Statement
sin^3(x) - cos^3(x) / sin(x) + cos(x) = csc^2(x) -cot(x) - 2cos^2(x) / 1 - cot^2(x)
Homework Equations
The Attempt at a Solution
I have attached
Alex1067 said:Ok thank you. I will try and that and see how it goes!
icystrike said:Here is the step by step solution.
I hope that you will refer it as reference only.
gabbagabbahey said:Your step by step solution is not only contrary to forum policy; but also contains errors. Please refrain from posting full solutions in the future.
What happened to the [itex]\sin x +\cos x[/itex] in the denominator? Did you divide it into [itex]\sin^2-\cos^2[/itex]?...If so, you should get [itex](\sin^3 x - \cos^3 x)(\sin x - \cos x)[/itex] for your numerator, not [itex](\sin^3 x - \cos^3 x)(\sin x + \cos x)[/itex]...Your next line seems to have this corrected though; so perhaps it was a typo.
The power reducing formulas in trigonometry are used to simplify expressions containing powers of trigonometric functions. They are:
To use the power reducing formulas, you need to replace any powers of trigonometric functions with the corresponding formula. Then, you can simplify the expression using algebraic manipulation and the properties of trigonometric functions.
The main difference between double angle and power reducing formulas is that double angle formulas involve doubling the angle, while power reducing formulas involve reducing the power of the trigonometric function.
Yes, power reducing formulas can be used to solve equations involving trigonometric functions. By simplifying the expression using the formulas, you can then use algebraic techniques to solve for the variable.
Yes, there are other techniques such as using trigonometric identities, trigonometric addition and subtraction formulas, and the unit circle. It is important to practice and familiarize yourself with these techniques to become proficient in simplifying difficult trig identities.