Evaluate this expression

BITSAT Tutorials › Trignometry questions › Evaluate this expression

Evaluate

3(\sin x- \cos x)^4 + 6(\sin x + \cos x)^2+ 4 \sin^6x+4 \cos^6x

IIT JEE 1975

#Mathematics #Trignometry

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7 Answers

1

MATRIX ·2009-03-21 09:25:32

hmmmmmmmm........[12][12][12]...........

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11

virang1 Jhaveri ·2009-03-21 09:31:17

3(sin²x + cos²x -2 cosxsinx)² + 6(sin²x +cox²x + 2cosxsinx)+4 sin⁶+4cos⁶x

= 3(1-2cosxsinx)²+6(1+2cosxsinsx) + 4(sin⁶x + cos⁶x)

= 3(1 + 4 cos²xsin²x -4sinxcosx) +6 + 12cosxsinx + 4(sin⁶x + cos⁶x)

= 3 + 12 cos²xsin²x - 12sinxcosx + 6 + + 12cosxsinx +4(sin⁶x + cos⁶x)

= 9 +12cos²sin²x + 4(sin⁶x + cos⁶x)

(sin²x +cos²x)³ = sin⁶x + cos⁶x + 3cos²xsin²x(sin²x + cos²x)

9 +12cos²sin²x + 4 - 12cos²sin²x
= 13
Which is the final answer

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1

MATRIX ·2009-03-21 09:33:07

[11][11][11].....[59]...........

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11

virang1 Jhaveri ·2009-03-21 09:39:51

Bhaiyya is it rite?

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Mani Pal Singh ·2009-03-21 09:40:40

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21

tapanmast Vora ·2009-03-21 09:54:34

tum logo ne galat kiya hai........

rite METHOD :

LET sinx = 1
==> cosx = 0;

so 3+6+4 = 13 NOW ITS CRRCT [4] [4]

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11

Mani Pal Singh ·2009-03-21 10:00:34

TAPAN
IIT WAS PURELY SUBJECTIVE IN 1975 [3][4]

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