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Simplifier :
A = cos (pi/6 + x) + cos (pi/6 - x)
B = sin (5pi/6 +x) - sin (7pi/6 + x)
C = tan (x + pi/4) × tan (x - pi/4)
Merci d'avance
Simplifier :
A = cos (pi/6 + x) + cos (pi/6 - x)
B = sin (5pi/6 +x) - sin (7pi/6 + x)
C = tan (x + pi/4) × tan (x - pi/4)
Merci d'avance
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Verified answer
A = cos(π/6 + x) + cos(π/6 - x) = cos(π/6)cos(x) - sin(π/6)sinx + cos(π/6)cos(x) - sin(π/6)sinx
A = √3/2 cos (x) - (1/2)sinx + √3/2 cos (x) + 1/2)sin (x) = √3 cos (x)
B = sin(5π/6 + x) - sin(7π/6 + x) = sin(5π/6)cos(x) + cos(5π/6)sin(x) - (sin(7π/6)cos(x) + cos(7π/6)sin (x)
B = 1/2) cos (x) - √3/2 sin (x) - (-1/2 cos (x) - √3/2 sin (x) = cos (x)
C = tan (x + π/4) x tan (x - π/4)
tan(x + π/4) = tan (x) + tan (π/4)]/(1 - tan (x)tan(π/4) = tan (x) + 1]/(1 - tan (x))
tan (x - π/4) = tan (x) - tan (π/4)]/(1 + tan (x)tan(π/4)) = tan (x) - 1]/(1 + tan (x)
C = tan (x) + 1]/(1 - tan (x)] x [tan (x) - 1]/(1 + tan (x) = - 1