Simplification ((SiNx + cosx-1) (SiNx cosx + 1) - 2cosx) / sin2x

Simplification ((SiNx + cosx-1) (SiNx cosx + 1) - 2cosx) / sin2x

[(sinx+cosx-1)(sinx-cosx+1)-2cosx]/sin2x=[(sinx)^2-(cosx-1)^2-2cosx]/sin2x=[(sinx)^2-(cosx)^2-1]/sin2x=[(sinx)^2-(cosx)^2-(sinx)^2-(cosx)^2]/sin2x =-2(cosx)^2/(2sinxcosx)=-cosx/sinx=-cotx

Simplification (SiNx + cosx-1) (SiNx cosx + 1) sin2x．

Original formula = (SiNx + 1-2sin2x2-1) (sinx-1 + 2sin2x2 + 1) sin2x = (2sinx2cosx2-2sin2x2) (2sinx2cosx2 + 2sin2x2) 4sinx2cosx2cosx2cosx = (cosx2 sinx2) (cosx2 + sinx2) • sinx2cosx2cosx = (cos2x2-sin2x2) sinx2cosx2 • cosx = cosx • sinx2cosx2 • co

Known function f (x) = SiNx / 2-2cosx / 2 = 0 (1) find the value of TaNx (2) find the value of cos2x / radical 2cos (π / 4 + x) xsinx

1. F (x) = SiNx / 2-2cosx / 2 = 0, you can get sin (x / 2) = 2cos (x / 2), so tan (x / 2) = (SiNx / 2) / (cosx / 2) = 1 / 2, so TaNx = (2tanx / 2) / [1-tan (x / 2) ^ 2] = 4 / 3.2. Molecular cos2x = (cosx) ^ 2 - (SiNx) ^ 2 = (SiNx + cosx) (SiNx cosx) denominator = √ 2 (cosxcos π / 4-sinxsin

Given SiNx / 2-2cosx / 2 = 0, find the value of cos2x / radical 2cos (π / 4 + x) SiNx

∵ SiNx / 2-2cosx / 2 = 0 ∵ SiNx / 2 = 2cosx / 2 ∵ TaNx / 2 = 2 ∵ TaNx = - 4 / 3 ∵ cos2x / root 2cos (π / 4 + x) SiNx = [(cosx) ^ 2 - (SiNx) ^ 2] / (cosx SiNx) * SiNx = (cosx SiNx) (cosx + SiNx) / (cosx SiNx) * SiNx = (cosx + SiNx) / SiNx = (1 / TaNx) + 1tanx = - 4 / 3 ∵ 1

SiNx = 2cosx, then the value of cos2x

sinx=2cosx
Square on both sides
(sinx) ²= 4(cosx) ²
1-(cosx) ²= 4(cosx) ²
(cosx) ²= 1/5
cos2x=2(cosx) ²- 1=2*1/5-1=-3/5
I hope it will help you

Known vector a = (1-tanx, 1), B = (1 + sin2x + cos2x, 0) It is known that a = (1-tanx, 1), B = (1 + sin2x + cos2x, 0). Note that the function f (x) = a * B, (1) find the analytical formula of the function f (x). (2) F（ α+ π / 8) √ 2 / 5, and α Belongs to (0, π / 2). Find F（ α） (both a and B are vectors)

(1) Because sin2x = 2sinxcosx, cos2x = 2cos ² X-1, so f (x) = AB = (1-tanx) (1 + sin2x + cos2x) = (1-tanx) (1 + 2sinxcosx + 2cos ²- 1)=(1-tanx)(2cos ² x-2sinxcosx)=(sinx+cosx)(2cos ² x-2sinxcosx)/cosx=2(sinx+cosx)(co...