Grade 12th passVectors

Cos X+CosY=1/3,SinX+SinY=1/4 then Sin (X+Y))=
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Krishnaveni

7 Years agoGrade 12th pass

2 Answers

Samyak Jain

7 Years ago

cosX + cosY = 1/3 $\Rightarrow$ 2 cos(X+Y)/2 cos(X–Y)/2 = 1/3 ...(1)

sinX + sinY = 1/4 $\Rightarrow$ 2 sin(X+Y)/2 cos(X–Y)/2 = 1/4 ...(2)

Divide (2) by (1)

[2 sin(X+Y)/2 cos(X–Y)/2] /[2 cos(X+Y)/2 cos(X–Y)/2] = (1/4)/(1/3)

tan(X + Y)/2 = 3/4.

We know that sin2x = 2 tanx / (1 + tan²x)

$\therefore$ sin(X + Y) = 2 tan(X + Y)/2 / (1 + tan²(X + Y)/2) = 2.(3/4) / (1 + 9/16)

= (3/2)(25/16)

sin(X + Y) = 24/25.

SANDEEP

4 Years ago

cosX + cosY = 1/3 \Rightarrow 2 cos(X+Y)/2 cos(X–Y)/2 = 1/3 ...(1)sinX + sinY = 1/4 \Rightarrow 2 sin(X+Y)/2 cos(X–Y)/2 = 1/4 ...(2)Divide (2) by (1)[2 sin(X+Y)/2 cos(X–Y)/2] /[2 cos(X+Y)/2 cos(X–Y)/2] = (1/4)/(1/3)tan(X + Y)/2 = 3/4.We know that sin2x = 2 tanx / (1 + tan2x)\therefore sin(X + Y) = 2 tan(X + Y)/2 / (1 + tan2(X + Y)/2) = 2.(3/4) / (1 + 9/16) = (3/2)(25/16) sin(X + Y) = 24/25.