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?????If cos(A+B) = 4/5 : sin(A-B) = 5/13 & A,B lie between 0 & 45*, then find the value of tan2A.

?????If cos(A+B) = 4/5 : sin(A-B) = 5/13 & A,B lie between 0 & 45*, then find the value of tan2A.

Grade:11

5 Answers

ankit agrawal
34 Points
9 years ago

tan2a=4

G Narayana Raju
51 Points
9 years ago
given,
cos(A+B) = 4/5, thus tan(A+B)=3/4.
sin(A-B)=5/13,thus tan(A-B)=5/12.
then tan(2A)=tan((A+B)+(A-B))
=(tan(A+B)+tan(A-B))/(1-tan(A+B)tan(A-B))
=(3/4+5/12)/(1-(3/4)(5/12))
=56/33.
Aditya Gupta
24 Points
4 years ago
cos(A+B)=4/5, thus tan(A+B)=3/4.
sin(A-B)=5/13,thus tan(A-B)=5/12.
then tan(2A)=tan((A+B)+(A-B))
= (tan(A+B)+tan(A-B))/(1-tan(A+B)tan(A-B))
= (3/4+5/12)/(1-(3/4)(5/12))
= 56/33.
Priyanshu
13 Points
2 years ago
Tan(a-b)=5/12 tan(a+b)=3/5Adding both eq.Tan(a-b+a+b)=5/12+3/5Tan(2a)=61/60:)
Krish Gupta
askIITians Faculty 82 Points
10 months ago
given,cos(A+B) = 4/5, thus tan(A+B)=3/4.sin(A-B)=5/13,thus tan(A-B)=5/12.then tan(2A)=tan((A+B)+(A-B))=(tan(A+B)+tan(A-B))/(1-tan(A+B)tan(A-B))=(3/4+5/12)/(1-(3/4)(5/12))=56/33
That works, I hope.

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