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laura1231
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Hi, I've tried to solve this equation:
$(2-\sqrt{2})(1+\cos x)+\tan x=0$
and I've tried everything but nothing works...Does anybody have an idea?Clever! (Bow)MarkFL said:If we use double-angle identities for cosine and tangent (where $u=\dfrac{x}{2}$), we have:
laura123 said:Thanks! There is another solution. When you use double-angle identities for cosine and tangent you have $x\neq \pi+2k\pi$, but this is also a solution of the equation.
laura123 said:Thanks! There is another solution. When you use double-angle identities for cosine and tangent you have $x\neq \pi+2k\pi$, but this is also a solution of the equation.
A trigonometric equation is an equation that contains one or more trigonometric functions, such as sine, cosine, tangent, or their inverses. These equations are used to solve for unknown angles or sides in triangles or other geometric shapes.
The basic trigonometric identities are sine squared plus cosine squared equals one, tangent equals sine over cosine, and cotangent equals cosine over sine. These identities are useful for simplifying and solving trigonometric equations.
To solve a trigonometric equation, you must isolate the trigonometric function and use the appropriate trigonometric identity to simplify it. Then, use inverse trigonometric functions or a calculator to solve for the variable.
Common mistakes when solving trigonometric equations include forgetting to use the appropriate trigonometric identity, using the wrong inverse trigonometric function, and not considering all possible solutions for the variable.
Trigonometric equations have many real-world applications, such as calculating distances and heights using angles and trigonometric functions, designing and building structures like bridges and buildings, and analyzing wave patterns in physics and engineering. They are also used in navigation, astronomy, and music theory.