Question

Решить уравнение sin(π cosx) = cos(π sin x).

Answer 1

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If sin(πcosx)=cos(πsinx), then sin2x=?

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Solution

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cos(πsinx)=sin(πcosx)

⇒cos(πsinx)=cos(π/2−πcosx)

So, πsinx=2nπ±(π/2−πcosx)

sinx=2n±(1/2−cosx)

Where π is any integer.

if n=0

sinx=1/2±cosx

sinx=−1/2+cosx or sinx=1/2−cosx

cosx−sinx=1/2 sinx+cosx=1/2

Squaring both sides,

1+sin2x=1/4 or 1−sin2x=1/4

sin2x=−3/4 or sin3/4

∴ sin2x=−3/4 or 3/4

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SIMILAR QUESTIONS

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If 2sin

2

((

2

π

)cos

2

x)=1−cos(πsin2x);x



=

2

(2n+1)π

,n∈I, then cos2x is equal to