54.6k views
0 votes
Complete the identity.
sin x/cos x + cos x/sin x =?

User GrpcMe
by
8.4k points

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
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories