Pitanje # 132a1

Pitanje # 132a1
Anonim

Odgovor:

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Obrazloženje:

# LHS = 1 + sin4x krevetić ((3pi) / 4-2x) + cos4x #

# = 1 sin4x + (krevetić ((3pi) / 4) * cot2x + 1) / (cot2x krevetić ((3pi) / 4)) * # cos4x

# = 1 sin4x + ((krevetić (pi-pi / 4) * cot2x + 1) / (cot2x krevetić (pi-pi / 4))) * # cos4x

# = 1 sin4x + (- krevetić (pi / 4) * cot2x + 1) / (cot2x - (- krevetić (pi / 4))) * # cos4x

# = 1 sin4x + (1-cot2x) / (1 + cot2x) + cos4x #

# = 1 sin4x + (1- (cos2x) / (sin2x)) / (1+ (cos2x) / (sin2x)) * # cos4x

# = 1 sin4x + (sin2x-cos2x) / (sin2x + cos2x) + cos4x #

# = 1 + (2 (sin2x * cos4x-cos4x * cos2x-sin4x * sin2x-sin4x * cos2x)) / (2 (sin2x + cos2x)) *

# = 1 + (sin (4x + 2x) -sin (4x-2 x) -cos (4x + 2x) -cos (4x-2 x) -cos (4x-2 x) + cos (4x + 2x) -sin (4x + 2x) -sin (4x-2 x)) / (2 (sin2x + cos2x) #

# = 1 + (sin6x-sin2x-cos6x-cos2x-cos2x + cos6x-sin6x-sin (2 x)) / (2 (sin2x + cos2x) #

# = 1 odustati ((2 (sin2x + cos2x)) / (2 (sin2x + cos2x))) #

# = 1-1 = 0 = RHS #