- #1
Veronica_Oles
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Homework Statement
cot2x + sec2x = tan2x + csc2x
Homework Equations
The Attempt at a Solution
I began by working on my left side.
I got up until
=cos^4x + sin^2x / sin^2x cos^2x
And unsure of where to go next.
You made a good start working on the LHS. Do the same to the RHS and see what you get.Veronica_Oles said:Homework Statement
cot2x + sec2x = tan2x + csc2x
Homework Equations
The Attempt at a Solution
I began by working on my left side.
I got up until
=cos^4x + sin^2x / sin^2x cos^2x
And unsure of where to go next.
On right side I got sin^4x + cos^2x / cos^2x sin^2x , I can't seem to get itSteamKing said:You made a good start working on the LHS. Do the same to the RHS and see what you get.
Compare the LHS to the RHS now. Do you notice anything in common?Veronica_Oles said:On right side I got sin^4x + cos^2x / cos^2x sin^2x , I can't seem to get it
L.S = cos^4x / sin^2x cos^2x + sin^2x / sin^2x cos^2xSteamKing said:Compare the LHS to the RHS now. Do you notice anything in common?
I'm having a problem seeing how you go from the expression above to the one below:Veronica_Oles said:L.S = cos^4x / sin^2x cos^2x + sin^2x / sin^2x cos^2x
= cos^2x / sin^2x + 1 / cos^2x
I see that you found the common denominator, but your numerator is incorrect.= cos^2x + sin^2x / sin^2x cos^2x
Same comments from the LHS calculations apply above.= 1 / sin^2x cos^2x
R.S = sin^4x / sin^2x cos^2x + cos^2x / sin^2x cos^2x
= sin^2x / cos^2x + 1 / sin^2x
= sin^2x + cos^2x / sin^2x cos^2x
= 1 / sin^2x cos^2x
Would this be the answer?
Veronica_Oles said:On right side I got sin^4x + cos^2x / cos^2x sin^2x
When writing "fractions" with an "in-line" format, one using the " / " character, you need to use parentheses to include (the entire numerator) / (the entire denominator).Veronica_Oles said:L.S = cos^4x / (sin^2x cos^2x) + sin^2x / (sin^2x cos^2x)
= cos^2x / sin^2x + 1 / cos^2x
= ( ? × cos^2x + sin^2x) / (sin^2x cos^2x)
= 1 / (sin^2x cos^2x)
R.S = sin^4x / (sin^2x cos^2x) + cos^2x / (sin^2x cos^2x)
= sin^2x / cos^2x + 1 / sin^2x ( No idea what you did here. Whatever, it's not legal.)
= (sin^2x + cos^2x) / (sin^2x cos^2x)
= 1 / (sin^2x cos^2x)
Would this be the answer?
The equation cot2x + sec2x = tan2x + csc2x is a trigonometric equation that involves the functions cotangent, secant, tangent, and cosecant. It is an identity that is often used in trigonometric proofs.
To solve for cot2x + sec2x = tan2x + csc2x, you can use algebraic manipulation and trigonometric identities. First, you can rearrange the terms to group the functions cot2x and tan2x together, as well as the functions sec2x and csc2x together. Then, you can use the trigonometric identity cot2x = 1/tan2x and sec2x = 1/cos2x to simplify the equation. Finally, you can use the Pythagorean identity sin2x + cos2x = 1 to further simplify the equation and solve for x.
The possible values of x that satisfy cot2x + sec2x = tan2x + csc2x are all real numbers except for values that make the denominators of the functions undefined. For example, x cannot equal 0 or π/2 because that would make the tangent and cotangent functions undefined. Additionally, x cannot equal π/4 or 3π/4 because that would make the secant and cosecant functions undefined.
Yes, you can use a calculator to solve for cot2x + sec2x = tan2x + csc2x. Most scientific calculators have trigonometric functions, as well as the ability to simplify and solve equations. However, it is important to understand the steps and principles behind the solution rather than relying solely on a calculator.
The equation cot2x + sec2x = tan2x + csc2x can be applied in various fields such as engineering, physics, and astronomy. For example, it can be used to calculate angles and distances in navigation and surveying. It can also be used in analyzing the motion of objects in physics and predicting the positions of celestial bodies in astronomy.