Question

Cos(x+y)=4/5 sin( x-y) =5/13 find tan2x where x, y lie bet 0,45degr

Answer 1

value of tan2x = 14/33

cos(x + y) = 4/5 , sin(x - y) = 5/13 then we have to find tan2x if (x, y) belongs to [0, 45°]

cos(x + y) = 4/5 = b/h

so, tan(x + y) = p/b = √(5² - 4²)/4 = 3/4 ....(1)

similarly, sin(x - y) = 5/13 = p/h

tan(x - y) = p/b = 5/√(13² - 5²) = 5/12 .....(2)

tan2x = tan{(x + y) + (x - y)}

= [tan(x + y) + tan(x - y)]/[1 - tan(x + y).tan(x - y)]

= [3/4 + 5/12 ]/[1 - 3/4 × 5/12]

= [14/12 ]/[(48 -15)/12]

= (14/33)

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