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Lets start and cover the two most used trigonometric formulas: Sin addition formula:sin( + ) = sin()cos() + cos()sin(), Cos addition formula:cos( + ) = cos()cos() - sin()sin(). \(\dfrac{\cot^2 x}{\csc x}=\csc x\sin x\), \(\dfrac{\sin x}{1\cos x}=\dfrac{1+\cos x}{\sin x}\), \(\csc\left(\dfrac{\pi}{2}x\right)=\sec x\), \(\tan\left(\dfrac{\pi}{2}x\right)=\tan x\), \(\dfrac{\csc x}{\sin x}\dfrac{\cot x}{\tan x}=1\), \(\dfrac{\tan ^2 x}{\tan ^2 x+1}=\sin ^2 x\), \((\sin x\cos x)^2+(\sin x+\cos x)^2=2\), \(\tan ^2 x+1+\tan x \sec x=\dfrac{1+\sin x}{\cos ^2 x}\), \(\cos ^2 x=\csc x \cos x \tan x+\cot x\), \(\dfrac{1}{1\sin x}\dfrac{1}{1+\sin x}=2\tan x \sec x\), \((\sin x\tan x)(\cos x\cot x)=(\sin x1)(\cos x1)\). Solved example of trigonometric identities, Applying the secant identity: $\displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}$, Applying the cosecant identity: $\displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}$, The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors, Obtained the least common multiple, we place the LCM as the denominator of each fraction and in the numerator of each fraction we add the factors that we need to complete, Applying the pythagorean identity: $\sin^2\left(\theta\right)+\cos^2\left(\theta\right)=1$, Combine and simplify all terms in the same fraction with common denominator $\cos\left(x\right)^2\sin\left(x\right)^2$, Since both sides of the equality are equal, we have proven the identity. Consequences on the military and provide other useful, relevant information report spouse. 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