# Prove q((p^2)-1)=2: Struggling to Crack the Math Problem

• MHB
• Wild ownz al
In summary, we can prove that q((p^2)-1) = 2 by using the given equations SinA + CosA = p and TanA + CotA = q, and solving for the unknown value.
Wild ownz al
If SinA + CosA = p and TanA + CotA = q, prove that q((p^2)-1) = 2. (Spent hours STILL could not figure out!)

Wild ownz al said:
If SinA + CosA = p and TanA + CotA = q, prove that q((p^2)-1) = 2. (Spent hours STILL could not figure out!)

Let us start from the LHS

$\sin\, A + \cos\,A = p$
square both sides
$(\sin\, A + \cos\,A)^2 = p^2$

or $\sin^2 A + 2 \sin\, A \cos\, A + cos^2 A = p^2$
or $1 +2 \sin\, A \cos\, A = p^2$
or $p^2 - 1 = 2 \sin\, A \cos\, A\cdots(1)$
from $2^{nd}$ condition
$\frac{\sin\, A}{\cos\, A} + \frac{\cos \, A}{\sin \, A} = q$
or $\frac{\sin^2 A+\cos^2 A}{\cos\, A\sin \, A} = q$
or $\frac{1}{\cos\, A\sin \, A} = q\cdots(2)$

multiplying (1) with (2) you get the result

## 1. How do I approach solving this math problem?

To solve this problem, you can start by substituting the given value of q into the equation. Then, you can simplify the equation by using the exponent rule for p^2 and the distributive property. From there, you can continue to manipulate the equation until you reach the desired solution of 2.

## 2. What are the key concepts needed to solve this problem?

To solve this problem, you will need to have a strong understanding of algebraic manipulation, specifically with exponents and the distributive property. You will also need to have a solid grasp of basic arithmetic operations.

## 3. Is there a specific order in which I should solve this problem?

While there is no specific order in which you must solve this problem, it may be helpful to start by simplifying the equation and then working towards the desired solution of 2. You may also find it helpful to break the problem down into smaller steps and tackle each step individually.

## 4. What are some common mistakes to avoid when solving this problem?

Some common mistakes to avoid when solving this problem include forgetting to use the exponent rule for p^2, not properly distributing the q value, and making arithmetic errors. It is also important to double-check your work and make sure you are following the correct steps.

## 5. Are there any helpful tips or tricks to solve this problem more efficiently?

One helpful tip to solve this problem more efficiently is to work backwards from the desired solution of 2. This can help guide your steps and make it easier to manipulate the equation. It may also be helpful to break the problem down into smaller, more manageable steps.

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