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if tan(A+B)=x and tan(A-B)=y find the value of tan 2A and tan2B
Most Upvoted Answer
if tan(A+B)=x and tan(A-B)=y find the value of tan 2A and tan2B
Given:
To find:
We can use the following trigonometric identities to find the value of tan 2A and tan 2B.
We can use the following identities to find the values of tan A and tan B:
Solving the above equations for tan A and tan B, we get:
Substituting the values of tan A and tan B in the identities of tan 2A and tan 2B, we get:
Simplifying the expressions for tan 2A and tan 2B, we get:
- tan(A B) = x
- tan(A-B) = y
To find:
- tan 2A
- tan 2B
Solution:
Using Trigonometric Identities
We can use the following trigonometric identities to find the value of tan 2A and tan 2B.
- tan 2A = 2tan A / (1 - tan² A)
- tan 2B = 2tan B / (1 - tan² B)
Finding tan A and tan B
We can use the following identities to find the values of tan A and tan B:
- tan(A B) = (tan A + tan B) / (1 - tan A * tan B) = x
- tan(A-B) = (tan A - tan B) / (1 + tan A * tan B) = y
Solving the above equations for tan A and tan B, we get:
- tan A = (x-y) / (1+xy)
- tan B = (x+y) / (1-xy)
Substituting tan A and tan B in the identities of tan 2A and tan 2B
Substituting the values of tan A and tan B in the identities of tan 2A and tan 2B, we get:
- tan 2A = 2 [(x-y) / (1+xy)] / [1 - {(x-y) / (1+xy)}²]
- tan 2B = 2 [(x+y) / (1-xy)] / [1 - {(x+y) / (1-xy)}²]
Simplifying the expressions for tan 2A and tan 2B
Simplifying the expressions for tan 2A and tan 2B, we get:
- tan 2A = (2x) / (1-x²-y²)
- tan 2B = (2y) / (1-x²-y²)
Answer:
- tan 2A = (2x) / (1-x²-y²)
- tan 2B = (2y) / (1-x²-y²)
Community Answer
if tan(A+B)=x and tan(A-B)=y find the value of tan 2A and tan2B
we can write 2a= (a+b)+(a-b) and 2b = (a+b)-(a-b)tan(2a) =tan( (a+b)+(a-b) ) = (tan(a+b) +tan(a-b) ) / ( 1-tan(a+b) tan(a-b)) = (x+y) / (1-xy)similarly tan(2b) =tan( (a+b)-(a-b) ) = (tan(a+b) - tan(a-b) ) / ( 1+ tan(a+b) tan(a-b)) = (x-y) / (1+xy)is this answer is right.I think it is right only.
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if tan(A+B)=x and tan(A-B)=y find the value of tan 2A and tan2B for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about if tan(A+B)=x and tan(A-B)=y find the value of tan 2A and tan2B covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for if tan(A+B)=x and tan(A-B)=y find the value of tan 2A and tan2B.
if tan(A+B)=x and tan(A-B)=y find the value of tan 2A and tan2B for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about if tan(A+B)=x and tan(A-B)=y find the value of tan 2A and tan2B covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for if tan(A+B)=x and tan(A-B)=y find the value of tan 2A and tan2B.
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