Simplify (2cos ^ 2x-1) (3cos ^ 2x-1) / cos2x

Simplify (2cos ^ 2x-1) (3cos ^ 2x-1) / cos2x

(2cos^2x-1)(3cos^2x-1)/cos2x
=cos2x(3cos^2x-1)/cos2x
=3cos^2x-1
=cos^2x+(2cos^2x-1)
=cos^2x+cos2x

Mathematical problem f (cosx) = cos2x f (SiNx) = - cos2x If you know that f (cosx) = cos2x, how is f (SiNx) = - cos2x derived? If you know, please write the process in detail. If you are correct, you will add more scores,

F(cosx)=cos2x=2cosx^2-1
Let y = cosx,
Then f (y) = 2Y ^ 2-1
F(sinx)=2sinx^2-1=-(1-2sinx^2)=-cos2x
Happy New Year!

The trigonometric function formula process of 3sin ^ 2 x + cos ^ 2 x = 2-cos2x

3sin^2 x+cos^2 x
=2sin^2 x+sin^2 x+cos^2 x
=2sin^2 x+1
=2+2sin^2 x-1
=2-cos2x

How to find x for a math expert cos2x-sin2x = 1 That's 2x, not square

cos2x-sin2x=cos^2x+sin^2x;
cos^2x-sin^2x-2sinxcosx=cos^2x+sin^2x;
-2cosx=2sinx;
tanx=-1;
x=-π/4+kπ

Half angle formula of SiNx cosx?

Sin2x=2Sinx*Cosx
Cos2x = cosx squared - SiNx squared = 1-2sinx squared = 2cosx squared-1

TaNx / 2 = SiNx / 1 + cosx = 1-cosx / SiNx

It is proved that Tan (x / 2) = sin (x / 2) / cos (x / 2)
=2sin(x/2)cos(x/2)/[cos(x/2)]^2
=sinx/(1+cosx)
=sinx(1-cosx)/[1-(cosx)^2]
=sinx(1-cosx)/(sinx)^2
=(1-cosx)/sinx

Let f (SiNx) = cos2x, find the expression of F (cosx)

f(sinX)=cos2X=1-2(sinX)^2
Qi
f(cosX)=1-2(cosX)^2=(sinX)^2-(cosX)^2=-cos2X

Our teacher has finished the double angle and dictated before class every time. Although I can understand the double angle, I always react slowly in dictation. I made six mistakes this time. I suspect that it is the most wrong in the whole class. I will have dictation again tomorrow. Please tell me if you have any tips for memorizing double angle,

Sine double angle formula:
sin2α = 2cosαsinα
Cosine double angle formula:
1.cos2A = 2cos²A-1
2.cos2A = 1−2sin²A
3.cos2A = cos²A−sin²A
Tangent double angle formula
tan2α = 2tanα/[1 - (tanα)²]

Several mathematical trigonometric function problems 1. Find the maximum value of the function f (x) = 2cos ^ 2x + 2sinxcosx + 1 on [0, π / 2] 2. Given the function f (x) = 2cosxsin (π / 2-x), find the monotone interval of F (x) 3. Known function f (x) = cos (2x - π / 3) + 2Sin (x - π / 4) sin (x + 4) (1) Find the minimum positive period of function f (x) and the equation of symmetry axis of image (2) Find the value range of function f (x) on the interval [- π / 12, π / 2] 4. The minimum positive period of the function f (x) = sin2wx + gen3sinwxsin (Wx + π / 2) (W > 0) is π (1) . find the value of W (2) Draw f (x) within a period =Seeking process and good man

1,f(x)=2cos^2x+2sinxcosx+1=sin2x+cos2x+2=√2sin(2x+π/4)+2.
Zero

On the formula of double angle in senior one mathematics How to use double angle formula to find the value of sine cosine tangent Given tan2 α = 1 / 3, find the value of Tan α

tan2α=2tana/1-tan^2a=1/3,
6 Tana = 1-tan ^ 2a, Tan ^ 2A + 6tana-1 = 0 is enough to solve the quadratic equation of one variable