Perform the addition 0 15. (1)/(1+cos x)+(1)/(1-cos x)

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Perform the addition 0 15.  (1)/(1+cos x)+(1)/(1-cos x)

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Write Expressions: Write down the expressions to be added. We have two expressions: (1)/(1+cos x) and (1)/(1-cos x).Find Common Denominator: Find a common denominator for the two expressions. The common denominator for (1+cos x) and (1-cos x) is (1+cos x)(1-cos x).Rewrite with Common Denominator: Rewrite each fraction with the common denominator. The first fraction becomes ((1-cos x)/((1+cos x)(1-cos x))) and the second fraction becomes ((1+cos x)/((1+cos x)(1-cos x))).Add Fractions: Add the two fractions. Now that they have a common denominator, we can add the numerators: (1-cos x) + (1+cos x).Simplify Numerator: Simplify the numerator. When we add (1-cos x) + (1+cos x), the cos x terms cancel out, leaving us with 1 + 1, which equals 2.Write Combined Fraction: Write the combined fraction. The combined fraction is now (2)/((1+cos x)(1-cos x)).Simplify Denominator: Simplify the denominator. We recognize that (1+cos x)(1-cos x) is the difference of squares, which simplifies to 1 - cos^2 x.Recognize Pythagorean Identity: Recognize the Pythagorean identity. We know that cos^2 x + sin^2 x = 1, so 1 - cos^2 x = sin^2 x.Substitute Identity: Substitute the identity into the denominator. The denominator becomes sin^2 x, so the fraction is now (2)/(sin^2 x).Write Final Form: Write the final simplified form. The final simplified form of the sum is (2)/(sin^2 x).

Perform the addition $0_{15}$ . $\newline$ $\frac{1}{1+\cos x}+\frac{1}{1-\cos x}$

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