Question

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Answer 1

Answer:

$\sqrt{15}$

Step-by-step explanation:

sinx/ siny=1/2 => sinx/2 =siny/2=a

sinx=a; siny=2a

cosx/cosy=3/2=>cosx/3=cosy/2=b

cosx=3b ; cosy=2b

tan(x+y)=sin(x+y)/cos(x+y) sin²x=a²

= sinx cosy + cosx × Siny / 1-cos²x=a²

cosx cosy- sinx siny 1-9b²=a²-------(2)

= (a) (2b)+(3b)(2a)/ sin²y= 4a²

6b² - 2a² 1-cos²y=4a²

1-4b²=4a²

= 8ab/ 1-4b²=4(1-9b²)

6b² -2a² 1-4b²=4-36b²

= 4ab/b²/ 3 - a²/b² 32b²=3

=4(a/b)/3-(a/b)² -------(1) b²=3/32

a²=1-27/32

a²=5/32

4( root5/3) / 3-5/3

= 4root5/3 /4/3

= 3root 5/3 ×root3/ root3

=3root15/3

= root15

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