Find 3tan^2A+4tan^2B for A,B Real Numbers

In summary, the formula for finding 3tan^2A+4tan^2B is 3tan^2A+4tan^2B=3tan^2A+4tan^2B, where A and B are real numbers. To solve for A and B in this equation, two additional equations involving A and B are needed. The equation can be simplified by using the trigonometric identity tan^2A=sec^2A-1. Using real numbers for A and B allows for a more accurate and applicable solution. This equation can be applied in real life in fields such as physics, engineering, and astronomy to calculate angles and distances.
  • #1
romsofia
597
310
1. Homework Statement A and B are real numbers satisfying 2(sinA+cosB)sinB=3-cosB. Find 3tan^2A+4tan^2B
2. Homework Equations Trig Identities
3. The Attempt at a Solution well, i expanded 3tan^2A+4tan^2B= 3sin^2A*cos^2B+4sin^2B*cos^2A all over cos^2A*cos^2B after that I am stuck :x
 
Last edited:
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  • #2
Are we to assume that "A" is the same as "a" and that "B" is the same as "b"?
 
  • #3
HallsofIvy said:
Are we to assume that "A" is the same as "a" and that "B" is the same as "b"?

yes, let me edit that :x
 

Related to Find 3tan^2A+4tan^2B for A,B Real Numbers

1. What is the formula for finding 3tan^2A+4tan^2B?

The formula for finding 3tan^2A+4tan^2B is 3tan^2A+4tan^2B = 3tan^2A+4tan^2B, where A and B are real numbers.

2. How do you solve for A and B in this equation?

To solve for A and B in this equation, you need to have two additional equations that involve A and B. From there, you can use algebraic methods to solve for A and B.

3. Can this equation be simplified?

Yes, this equation can be simplified by using the trigonometric identity tan^2A = sec^2A - 1. This will result in a simpler equation to solve for A and B.

4. What is the significance of using real numbers for A and B?

The use of real numbers for A and B in this equation allows for a more accurate and precise calculation. It also ensures that the solution is applicable in real-world situations.

5. How can this equation be applied in real life?

This equation can be applied in real life in various fields such as physics, engineering, and astronomy. It can be used to calculate angles and distances in real-world scenarios where trigonometry is involved.

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