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
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