Vraag # 9a6e1

Vraag # 9a6e1
Anonim

Antwoord:

Zie onder.

Uitleg:

# LHS = (1 + SiNx-cosx) ^ 2 / (1 + + cosx SiNx) ^ 2 #

# = (1 + 2 (SiNx-cosx) + (SiNx-cosx) ^ 2) / (1 + 2 (SiNx cosx +) + (+ cosx SiNx) ^ 2 #

# = (1 + 2 (SiNx-cosx) + sin ^ 2x + 2sinx * cosx + cos ^ 2x) / (1 + 2 (SiNx + cosx) + (sin ^ 2x + 2sinx * cosx + cos ^ 2x) #

# = (2 + 2 (SiNx-cosx) + 2sinx * cosx) / (2 + 2 (SiNx + cosx) + 2sinx * cosx) #

# = (1 + SiNx-cosx + sinx * cosx) / (1 + sinx + + cosx sinx * cosx) #

# = (1-cosx sinx + (1 + sinx)) / (1 + cosx sinx + (1 + sinx) #

# = ((1-cosx) (1 + sinx)) / ((1 + cosx) (1 + SiNx)) #

# = (1-cosx) / (1 + cosx) = RHS #

# LHS = (1 + SiNx-cosx) ^ 2 / (1 + + cosx SiNx) ^ 2 #

# = (2sin ^ 2 (x / 2) + 2sin (x / 2) cos (x / 2)) ^ 2 / (2cos ^ 2 (x / 2) + 2sin (x / 2) cos (x / 2)) ^ 2 #

# = (4sin ^ 2 (x / 2) te annuleren ((sin (x / 2) + cos (x / 2)) ^ 2)) / (4cos ^ 2 (x / 2) te annuleren ((sin (x / 2) + cos (x / 2)) ^ 2)) #

# = (Cancel2 (1-cosx)) / (cancel2 (1 + cosx)) = RHS #