Trigonometry> Compound angles...

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

ankit agrawal , 12 Years ago

Grade 11

5 Answers

ankit agrawal

Last Activity: 12 Years ago

tan2a=4

Approved

G Narayana Raju

Last Activity: 12 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.

Approved

Aditya Gupta

Last Activity: 8 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

Last Activity: 6 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

Last Activity: 4 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

That works, I hope.