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Trignometry

New kid on the Block

 Joined: 31 Jan 2011 Post: 1
31 Jan 2011 16:06:18 IST
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if sin x + cos x =1 the find the value of (sin x)^3+(cos x )^3.
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Trigonometry

if sin x + cos x =1 the find the value of (sin x)^3+(cos x )^3.

Cool goIITian

Joined: 25 Sep 2010
Posts: 85
31 Jan 2011 16:17:45 IST
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Blazing goIITian

Joined: 16 Jan 2010
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31 Jan 2011 19:13:26 IST
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If x < 900, then x = 00 or 900

Thus, two cases

(sin 0)3 + (cocs 0)3 = 1

(sin 90)3 + (cos 90)3 = 1

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Joined: 19 Feb 2009
Posts: 1958
31 Jan 2011 19:48:25 IST
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Hello !

(sinx+cosx)^2 = 1

sin^2(x) + cos^2(x) + 2.sinx.cosx = 1

sin2x = 0

So ...2x = n*pi

So .. x = n*pi/2

Now ...sin^3x + cos^3x  = M

For .... (n/2) = odd  => then cosx = -1 ...And   M = -1 ...{ for case n = 10 , n=6 , n = 2 ......}

For ...(n/2) = even => then cosx= 1  And  M = 1.....{for case n=4,n=8 .....and so on ..}

For other case ...M = 0

I hope it is clear now

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31 Jan 2011 20:05:10 IST
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Blazing goIITian

Joined: 16 Jan 2010
Posts: 318
1 Feb 2011 15:11:12 IST
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sin x + cos x = 1

on squaring both the sides,

sinx.cosx = 0

Again, sin3x + cos3x = (sinx + cosx)(1 - sinx.cosx) = (1)(1 - 0) = 1 Ans.

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