Rewrite with only sin x and cos x. sin 2x - cos 2x

Asked by maham237 @ 17/12/2020 in Mathematics viewed by 324 People

10. Rewrite with only sin x and cos x. (1 point)
sin 2x - cos 2x

a) 2 sinx cosx - 1 + 2 sin2x
b) 2 sin x cos2x - 1 + 2 sin2x
c) 2 sin x cos2x - sin x + 1 - 2 sin2x
d) 2 sin x cos2x - 1 - 2 sin2x

11. Find the exact value by using a half-angle identity. (1 point)
sin 22.5°

a) negative one half times the square root of quantity two plus square root of two.
b) one half times the square root of quantity two plus square root of two.
c) negative one half times the square root of quantity two minus square root of two.
d) one half times the square root of quantity two minus square root of two

15. Verify the identity. (1 point)
cot x minus pi divided by two. = -tan x

NEED HELP ASAP PLEASEEEE!!!

Answered by maham237 @ 17/12/2020

10. Rewrite with only sin x and cos x.
sin 2x - cos 2x

sin2x =
2sinxcosx

cos2x = (cosx)^2 - (sinx)^2 = 2(cosx)^2 -1 = 1-
2(sinx)^2

sin2x- cos2x=2sinxcosx-(1- 2(sinx)^2=2sinxcosx-1+2(sinx)^2

sin2x- cos2x=2sinxcosx-1+2(sinx)^2

the answer is the letter b) 2 sin x cos2x - 1
+ 2 sin2x

11. Find the exact value by using a half-angle identity. sin 22.5°Using the half angle formula you get:sin2(θ)=12[1−cos(2θ)]if θ=22.5° then 2θ=45°so you get:sin2(22.5°)=12[1−cos(45°)]sin2(22.5°)=12[1−√2/2]=2−√24and square root both sides:sin(22.5°)=±√2−√24=±0.382so
sin(22.5°)=0.382the answer is the letter D) one half times the square root of quantity two minus square root of two
15. Verify the identity.
cot x minus pi divided by two. = -tan x
Cot(x-pi/2)=-tan(x)
sin(A − B) = sin A cos B − cos A sin B
sin(x – pi/2) = sin x cos (pi/2) − cos x sin (pi/2)=-cosx

cos(A − B) = cos A cos B − sin A sin B
cos(x− pi/2) = cos x cos pi/2 − sin x sin pi/2=-sinx
Cot(x-pi/2)=cos(x-pi/2)/sin(x-pi/2)
= (-sinx)/(-cosx)=-tanx--------------ok

Rewrite with only sin x and cos x. sin (3x) - cos (x) please guide me with showing work because the process of substituting is what i'm having difficulties with

Asked by maham237 @ 27/12/2020 in Mathematics viewed by 316 persons

Rewrite with only sin x and cos x. sin 2x - cos 2x

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