CBSE Class 11-science Answered
Q)tan(A + B)=1 and tan(A-B)=1/7
Find tanA and tan B?
Asked by yask12 | 01 Aug, 2010, 04:04: PM
Expert Answer
Dear Student,
Here,
tan(A+B) = 1
which means
tan A + tan B
______________ = 1
1 - tan A tan B
tan A + tan B = 1-tan A tan B
tan A + tan B - 1+ tan A tan B = 0
Also, tan(A - B) = 1/7
So,
tan A - tan B
_____________ = 1/7
1+tan A tan B
7tan A - 7tan B = 1 + tan A tan B
7tan A - 7tan B - 1 - tan A tan B = 0
tan A + tan B-1+tan A tan B=0
7tan A-7tan B-1-tan A tan B=0
Let
tan A = x and tan B = y
x + y - 1 + xy = 0
x + y + xy = 1 ...........(a)
7x - 7y - 1 - xy = 0
7x - 7y - xy = 1 ..........(b)
From equation (a)
x + y + xy = 1
x + xy = 1 - y
x(1 + y) = 1 - y
x = (1-y)/(1+y)
Replacing this value of x in equation (b), we get
x + xy = 1 - y
x(1 + y) = 1 - y
x = (1-y)/(1+y)
Replacing this value of x in equation (b), we get
7(1 - y)/(1 + y) - 7y - y(1 - y)/(1 + y) = 1
[(7-7y)/1+y] -7y - (y - y2)/(1+y) = 1
(7 - 7y)/(1 + y) - (y - y2)/(1+y)=1 + 7y
7 - 7y - y+y2
_____________ =1 + 7y
1 + y
7 - 8y + y2 = (1 + 7y)(1 + y)
7 - 8y + y2 = 1 + 8y + 7y2
6y2 + 16y - 6 = 0
6y2 + 16y - 6 = 0
(6y - 2)(y + 3)=0
y = 1/3 or y = -3(rejected)
So, when y = 1/3
x = (1 - y)/(1+y)
x = (1 - 1/3)/(1+1/3)
x = 1/2
Hence, tan A=1/2 and tan B=1/3
Regards,
Team Topper Learning
Answered by | 01 Aug, 2010, 06:43: PM
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