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Complete the identity.
sin x/cos x + cos x/sin x =?

User GrpcMe
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1 Answer

6 votes

Answer:

2csc(2x)

Explanation:

When simplifying the given expression, we can start by finding a common denominator for the fractions. The common denominator for sin x and cos x is cos x * sin x.

Rewriting the expression using the common denominator, we have:

(sin x * sin x)/(cos x * sin x) + (cos x * cos x)/(sin x * cos x)

Simplifying the fractions, we get:

sin^2(x)/(cos x * sin x) + cos^2(x)/(sin x * cos x)

Now, let's simplify each fraction individually:

sin^2(x)/(cos x * sin x) can be simplified to (sin x / cos x)

cos^2(x)/(sin x * cos x) simplifies to (cos x / sin x)

Now, combining the simplified fractions, we have:

(sin x / cos x) + (cos x / sin x)

To combine these fractions, we need a common denominator, which is cos x * sin x:

[(sin x * sin x) + (cos x * cos x)] / (cos x * sin x)

Using the Pythagorean identity sin^2(x) + cos^2(x) = 1, we can simplify the numerator:

(1) / (cos x * sin x)

Therefore, the simplified form of the expression is 1 / (cos x * sin x), or 2csc(2x)

User Nurul Akter Towhid
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