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if sin2x+sin2y=1/3 and cos2x+cos2y=1/2 than prove that tan(x+y)=2/3

if sin2x+sin2y=1/3 and cos2x+cos2y=1/2 than prove that tan(x+y)=2/3

Grade:10

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
3 years ago
Dear Student

By using formulas
sin C +sin D = 2 sin (C +D)/2 cos (C -D)/2
cos C +cos D = 2 cos (C +D)/2 cos (C -D)/2
sin2x+sin2y= 2 sin (x+y) cos ( x- y ) = 1/3 ….....(1)
cos2x+cos2y= 2 cos ( x+y) cos( x –y )= 2/3 ........(2)

dividing equation 2 by 1
sin2x+sin2y=(1/3)
cos2x+cos2y (1/2)

2 sin (x+y) cos ( x- y ) = 1/3
2 cos ( x+y) cos( x –y ) 1/2
tan(x+y) = 2/3

Hence, Proved



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