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Trignometry

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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.

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

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rishabh

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31 Jan 2011 16:17:45 IST

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rahulmishra

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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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Yagyadutt Mishra

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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

Hari Shankar

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31 Jan 2011 20:05:10 IST

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rahulmishra

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1 Feb 2011 15:11:12 IST

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But what about this?

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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