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In a triangle ABC,C=90 then the equation whose roots are tanA,tanB is?
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In a triangle ABC,C=90 then the equation whose roots are tanA,tanB is?
Given information:
In triangle ABC, angle C is 90 degrees.
To find:
The equation whose roots are tanA and tanB.
Explanation:
1. Relationship between angles and tangents:
In a right-angled triangle, we can use the tangent function to relate the angles and sides of the triangle. The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side.
2. Relationship between angles and their tangents:
Since we are given that angle C is 90 degrees, we know that it is a right angle. Let's consider angles A and B, which are the other two angles in the triangle. The sum of the angles in a triangle is always 180 degrees. Therefore, A + B = 180 - C = 180 - 90 = 90 degrees.
3. Relationship between tangents of complementary angles:
The tangent function has a special property for complementary angles. If two angles are complementary, the tangent of one angle is equal to the reciprocal of the tangent of the other angle. In other words, if A and B are complementary angles, then tan(A) = 1/tan(B) and tan(B) = 1/tan(A).
4. Relationship between angles and their tangents in the given triangle:
In our given triangle ABC, angle C is 90 degrees, so angles A and B are complementary. Using the property mentioned above, we can write the following equations:
tan(A) = 1/tan(B) ...(1)
tan(B) = 1/tan(A) ...(2)
5. Finding the equation with roots tan(A) and tan(B):
To find the equation whose roots are tan(A) and tan(B), we need to eliminate the denominators in equations (1) and (2). We can do this by multiplying both sides of equation (1) by tan(B) and both sides of equation (2) by tan(A):
tan(A) * tan(B) = 1 ...(3)
tan(A) * tan(B) = 1 ...(4)
6. Combining the equations:
By combining equations (3) and (4), we can write the final equation:
tan(A) * tan(B) - 1 = 0
This equation has roots tan(A) and tan(B), as desired.
Summary:
In a right-angled triangle ABC with angle C = 90 degrees, the equation whose roots are tan(A) and tan(B) is tan(A) * tan(B) - 1 = 0. This equation is derived from the relationship between complementary angles and their tangents.
In triangle ABC, angle C is 90 degrees.
To find:
The equation whose roots are tanA and tanB.
Explanation:
1. Relationship between angles and tangents:
In a right-angled triangle, we can use the tangent function to relate the angles and sides of the triangle. The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side.
2. Relationship between angles and their tangents:
Since we are given that angle C is 90 degrees, we know that it is a right angle. Let's consider angles A and B, which are the other two angles in the triangle. The sum of the angles in a triangle is always 180 degrees. Therefore, A + B = 180 - C = 180 - 90 = 90 degrees.
3. Relationship between tangents of complementary angles:
The tangent function has a special property for complementary angles. If two angles are complementary, the tangent of one angle is equal to the reciprocal of the tangent of the other angle. In other words, if A and B are complementary angles, then tan(A) = 1/tan(B) and tan(B) = 1/tan(A).
4. Relationship between angles and their tangents in the given triangle:
In our given triangle ABC, angle C is 90 degrees, so angles A and B are complementary. Using the property mentioned above, we can write the following equations:
tan(A) = 1/tan(B) ...(1)
tan(B) = 1/tan(A) ...(2)
5. Finding the equation with roots tan(A) and tan(B):
To find the equation whose roots are tan(A) and tan(B), we need to eliminate the denominators in equations (1) and (2). We can do this by multiplying both sides of equation (1) by tan(B) and both sides of equation (2) by tan(A):
tan(A) * tan(B) = 1 ...(3)
tan(A) * tan(B) = 1 ...(4)
6. Combining the equations:
By combining equations (3) and (4), we can write the final equation:
tan(A) * tan(B) - 1 = 0
This equation has roots tan(A) and tan(B), as desired.
Summary:
In a right-angled triangle ABC with angle C = 90 degrees, the equation whose roots are tan(A) and tan(B) is tan(A) * tan(B) - 1 = 0. This equation is derived from the relationship between complementary angles and their tangents.
Community Answer
In a triangle ABC,C=90 then the equation whose roots are tanA,tanB is?
C=90
since,we know that
in triangle a+b+c=90
then a+b+90=90
a+b=0
since tan(a+b)=(tan a + tan b)/1- tan a tan b
tan 0 = (tan a + tan b)/1- tan a tan b
0= (tan a + tan b)/1- tan a tan b
tan a + tan b=0 ans.
since,we know that
in triangle a+b+c=90
then a+b+90=90
a+b=0
since tan(a+b)=(tan a + tan b)/1- tan a tan b
tan 0 = (tan a + tan b)/1- tan a tan b
0= (tan a + tan b)/1- tan a tan b
tan a + tan b=0 ans.
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In a triangle ABC,C=90 then the equation whose roots are tanA,tanB is? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about In a triangle ABC,C=90 then the equation whose roots are tanA,tanB is? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a triangle ABC,C=90 then the equation whose roots are tanA,tanB is?.
In a triangle ABC,C=90 then the equation whose roots are tanA,tanB is? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about In a triangle ABC,C=90 then the equation whose roots are tanA,tanB is? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a triangle ABC,C=90 then the equation whose roots are tanA,tanB is?.
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