1Hey anyone there ready to help me??
Guys solve it.... i've tried it but is not gettin the correct answer. Please also write the steps.
1) If sin x + sin y = 3(cos y - cos x), then find the value of sin3x + sin3y ?
2) If sin (x/2) + cos (x/2) = -1/2 , 3pie/2 < x < 2pie, then the value of sin2x?
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1My answer is coming out to be 0 for sin3x+sin3y. Is it right ? If yes then i can give the explanation.
62Rahul but that does not mean that this expression will be always zero..
be careful in such multiple correct answer questions.....
1sin x+3cos x= 3cos y - sin y
or, √10(1√10sin x + 3√10cos x) = √10(3√10cos y - 1√10sin y)
Let 1√10= cos α
Hence 3√10= sin α
Hence sin(α+x) = sin(α-y)
or, 2 sinx+y2 cos 2α+x-y2 = 0
or, sin x+y2=0
or,x=-y
or,sin3x = -sin 3y
Hence sin 3x+sin 3y = 0.
1there are 2 solutions ...
sin x + sin y=3 (cos y- cos x)
=> 2 sin{(x+y)/2} cos {(x-y)/2}= 6 sin {(x+y)/2} sin {(x-y)/2}
either sin {(x+y)/2}=0 or,tan {(x-y)/2}=1/3
aveek has taken only d first solution....but we have to take also the second solution into account
1maths_psy....wht can u do with the tan function.....how can u bring it to sin when u have a simpler expression before ur eyes ?
1both are answers until d latter is found out to be an extranious root (i,e which dus not satisfy d original solution)...hav to check whether d second 1 is an extranious root or not... we can get value of x and y through general solution.....
1But do u really need to take a step more for an mcq question....when u've already got the answer.....? ne ways ......ur solution is more complete than mine...............:-)
1dont mind aveek....in case of objective paper u would have saved a lot of time......but be carefull the next time onwards in case of multiple correct answers...........
1yes,in case of multiple correct answers u would hav got wrong if u ticked only d 1st 1
1Thanks guys. i too solved the question. And got the answers to both the questions.
However for the 1st question, I only got answer 0.
2nd question has answer -3√7/8