- #1
kasse
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Which trigonometric identitiy are used to transform 2(cos(x))^2+2cos(x)sin(x) into 0?
kasse said:Sorry, I gave you the wrong eq. Solved in on my own here.
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Transforming trigonometric identities helps simplify complex trigonometric expressions and equations, making them easier to solve. This is especially useful when working with trigonometric equations in calculus and other higher level math courses.
To solve this equation, you need to use trigonometric identities to simplify the expression. In this case, you can use the double angle identity for cosine (cos2x = 1 - 2sin^2x) to rewrite the equation as 2(1-2sin^2x)+2sinx=0. Then, you can use the quadratic formula to solve for sinx, and then use inverse trigonometric functions to find the solutions for x.
Some common trigonometric identities used in transforming equations include the Pythagorean identities (sin^2x + cos^2x = 1, tan^2x + 1 = sec^2x, cot^2x + 1 = csc^2x), the double angle identities (sin2x = 2sinxcosx, cos2x = cos^2x - sin^2x), and the half angle identities (sin(x/2) = ±√[(1-cosx)/2], cos(x/2) = ±√[(1+cosx)/2]).
Trigonometric equations often have multiple solutions, and sometimes the process of transforming the equation can introduce extraneous solutions, which are solutions that do not satisfy the original equation. Checking for extraneous solutions helps ensure that you have found all the correct solutions to the equation.
One tip for solving equations involving trigonometric identities is to try to simplify the expression as much as possible before attempting to solve. This can involve using identities, factoring, or manipulating the equation in other ways. Additionally, it is important to be familiar with common trigonometric identities and how to apply them in different situations.