# Solving the Mystery of cot2x & cosec2x

• ibysaiyan
In summary: Then take the square root of both sides to get csc(2x) = 2. Finally, solve for x using the reciprocal function of cosecant.
ibysaiyan

## Homework Statement

this time i have posted two questions on a post, instead of me creating posts all over the forum.

a)cot^2x + cosec^2x = 7
b) (2 cosec^2)2x + cot2x =3
find out the solutions.

## Homework Equations

cosec^2 = 1+ cot^2

## The Attempt at a Solution

a) cot^2x + cosec^2x = 7
cosec^2-1 + cosec^2 = 7
2cosec^2x = 8
now i thought of solving it by the difference of squares?
couldn't solve it =/
b) totally cluesless as this one has 2 after function cot i.e cot2x =/

ibysaiyan said:

## Homework Statement

this time i have posted two questions on a post, instead of me creating posts all over the forum.

a)cot^2x + cosec^2x = 7
b) (2 cosec^2)2x + cot2x =3
It's not very clear what the equation above is saying. You are at least using parentheses, but not in the most helpful way.
Is this supposed to be 2csc^2(2x) + cot(2x) = 3?

If so, you should replace csc(2x) with 1/sin(2x) and cot(2x) with cos(2x)/sin(2x).
ibysaiyan said:
find out the solutions.

## Homework Equations

cosec^2 = 1+ cot^2

## The Attempt at a Solution

a) cot^2x + cosec^2x = 7
cosec^2-1 + cosec^2 = 7
2cosec^2x = 8
now i thought of solving it by the difference of squares?
So csc^2(2x) = 4
Or 1/[sin^2(2x)] = 4
Can you take it from there?
ibysaiyan said:
couldn't solve it =/
b) totally cluesless as this one has 2 after function cot i.e cot2x =/

sorry as i am pretty newbie with latex =/ hmm i don't get it, how did you end up with = 4? and yea i got to say.. that question doesn't make sense well the way i typed makes it more complicated (looking)

Divide both sides of the equation by 2 to get csc^2(2x) = 4.

## 1. What is cot2x and cosec2x?

Cot2x and cosec2x are trigonometric functions that are used to find the ratios between the sides of a right triangle. Cot2x is the reciprocal of the tangent function, while cosec2x is the reciprocal of the sine function.

## 2. Why is solving the mystery of cot2x and cosec2x important?

Understanding cot2x and cosec2x is important because they are essential in solving many mathematical and scientific problems. They are also used in various fields such as engineering, physics, and navigation.

## 3. How do you solve equations involving cot2x and cosec2x?

To solve equations involving cot2x and cosec2x, you need to use the trigonometric identities and properties related to these functions. You can also use a calculator or reference table to find the values of cot2x and cosec2x for specific angles.

## 4. What are some common mistakes when solving problems involving cot2x and cosec2x?

One common mistake is forgetting to check the domain of the problem. Since cot2x and cosec2x involve division, the values of x must be within a certain range to avoid undefined results. Another mistake is not simplifying the equations before solving them, which can lead to incorrect answers.

## 5. How can I improve my understanding of cot2x and cosec2x?

To improve your understanding of cot2x and cosec2x, you can practice solving various problems involving these functions, use online resources and tutorials, and seek help from a teacher or tutor if needed. It is also helpful to have a strong foundation in trigonometry and understand the basics of other trigonometric functions.

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