Sin ^ 2x + cos ^ 2 + sin2x = 1, what is SiNx + cosx equal to

Sin ^ 2x + cos ^ 2 + sin2x = 1, what is SiNx + cosx equal to

Because sin2x = 2sinxcosx
sin^2x+cos^2x+2sinxcosx=1
(sinx+cosx)^2=1
So SiNx + cosx = ± 1

As the title, Verification: sin2x / [(SiNx + cosx-1) (SiNx + 1-cosx)] = cot (x / 2)

sin2x/ [(sinx+cosx-1)(sinx+1-cosx)]=sin2x/ [(sinx-(1-cosx)(sinx+1-cosx)]=sin2x/ [(sin^2x-(1-cosx)^2]=sin2x/ [sin^2x-1-cos^2x+2cosx]=sin2x/ [sin^2x-(sin^2x+cos^2x)-cos^2x+2cosx]=sin2x/ [-2cos^2x+2cosx]...

If the analytical formula of function f (x) is f (x) = 2tanx - (2Sin ^ 2 (x / 2) - 1) / (SiNx / 2 * cosx / 2) 30 - resolution time: 12:34, November 3, 2007 1. If the analytical formula of function f (x) is f (x) = 2tanx - (2Sin ^ 2 (x / 2) - 1) / (SiNx / 2 * cosx / 2) Then f (π / 12) is 2. Known α Is an acute angle, and sin α= 4 / 5 (1) find sin ^ 2 + sin2 α/ cos^2 α + cos2 α Value of (answer 20) （2）tan( α- 5 π / 4) (answer 1 / 7)

1) F (x) = 2tanx - (2Sin ^ 2 (x / 2) - 1) / (SiNx / 2 * cosx / 2) f (x) = 2tanx + cos X / (1 / 2 * SiN x) = 2tanx + 2 Cotx = 2 [(SiN x / cos x) + (cos X / SiN x)] = 4 / sin (2x) bring π / 12 in, = 8 1) find sin ^ 2 + sin2 α/ cos^2 α + cos2 α sin α= 4/...

Let f (x) = m (cosx + SiNx) ^ 2 + 1-2sin ^ 2 x, X belongs to R and y = f (x) The image passes through the point (Pie / 4,2) 1 to find the value of the real number m, 2 to find the minimum value of the function f (x) and the set of X at this time

F (x) = m (sin ^ 2x + cos ^ 2x) + msin2x + cos2x = m + msin2x + cos2xf (π / 4) = 2 = m + m, (sin π / 2 = 1, cos π / 2 = 0) M = 1F (x) = 1 + sin2x + cos2x = 1 + √ 2Sin (2x + π / 4) the minimum value is 1 - √ 2. At this time, 2x + π / 4 = 2K π + π 2x = 2K π + 3 π / 4x = k π + 3 π / 8, K ∈ Z

Known function f (x) = (SiNx + cosx) 2 (1) Find the minimum positive period of function f (x), and use the "five point method" to draw the diagram of function f (x) in one period; (2) Find the maximum value of function f (x) and the set of X when making function f (x) obtain the maximum value

（!）f（x）=sin2x+2sinx•cosx+cos2x=1+sin2x∴T=π．
list
Tracing line
(2) The necessary and sufficient condition for f (x) to obtain the maximum value is sin2x = 1, and the maximum value of F (x) is 2. At this time, 2x = π
2+2kπ，k∈Z，x=π
4+kπ．
When the function f (x) gets the maximum value, the set of X is {x | x = π
4+kπ，k∈Z}．

Function f (x) = 1-2sin ² The maximum value and period of (x / 2) + SiNx (x ∈ R) are?

(friendly tips: cos (2x) = 1-2sin ² x)
f(x)=cosx+sinx=(√2)sin(x+π/4)
The maximum value must still be √ 2, and the period T = 2 π / 1 = 2 π