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factor trigonometric expression and simplify: 1 - 2sin^2x + sin^4x = ? use a sum

ID: 2905551 • Letter: F

Question

factor trigonometric expression and simplify:

1 - 2sin^2x + sin^4x = ?

use a sum or difference identify to find the exact value:

sin (x + 45 degree)

use an identity to write the expression as a single trigonometric function or as a single number:

(2 tan (15 degrees)) / (1 - tan^2 (15 degrees))

sin 8x cos 8x

write the product as a sum or difference of trigonoetric functions:

2 cos 6x cox 2x

find thw exact value using half-angle identity:

cos 22.5 degrees

sin 75 degrees

please help! im not sure how to do these and if im doing them wrong!!!

explanitory answers are highly appriciated!!

thank you!

Explanation / Answer

1)

1 - 2sin^2x + sin^4x = ((sin x)^2)^2 - 2(sin x)^2 +1

=((sin x)^2 -1) ^2

2)sin (x + 45 degree) =sinx cos 45 +cosx sin 45

=(sinx *1/sqrt2 +cosx *1/sqrt2 )

=(1/sqrt2)(sinx +cosy)

3)

(2 tan (15 degrees)) / (1 - tan^2 (15 degrees))

=tan(15 +15)

=tan30

=sqrt3

sin 8x cos 8x

=(1/2)*2*sin 8x cos 8x

=(1/2) sin 16x

2 cos 6x cos 2x

=cos(6x+2x) +cos(6x -2x)

=cos8x +cos4x