1. Buktikan tiap identitas trigonometri berikut
[tex] {( \sec( \alpha ) )}^{2} - {( \sin( \alpha ) )}^{2} {( \sec( \alpha ) )}^{2} = 1 \\ {( \sec( \alpha )) }^{2} (1 - {( \sin( \alpha ) )}^{2} ) = 1 \\ \frac{1}{ {( \cos( \alpha ) )}^{2} } ( { (\cos( \alpha )) }^{2} = 1 \\ 1 = 1[/tex]
[tex] \tan^{2} ( \alpha ) \cos^{2} ( \alpha ) + \cot^{2} ( \alpha ) \sin^{2} ( \alpha ) = 1 \\ \frac{ \sin^{2} ( \alpha ) }{ \cos ^{2} ( \alpha ) } \cos^{2} ( \alpha ) + \frac{ \cos^{2} ( \alpha ) }{ \sin^{2} ( \alpha ) } \sin^{2} ( \alpha ) = 1 \\ \sin^{2} ( \alpha ) + \cos^{2} ( \alpha ) = 1 \\ 1 = 1[/tex]
[tex] \frac{1 - \sin( \alpha ) }{ \cos( \alpha ) } \times \frac{1 + \sin( \alpha ) }{1 + \sin( \alpha ) } \\ = \frac{1 - \sin^{2} ( \alpha ) }{ \cos( \alpha ) (1 + \sin( \alpha )) } \\ = \frac{ \cos ^{2} ( \alpha ) }{ \cos( \alpha )(1 + \sin( \alpha )) } \\ \frac{ \cos( \alpha ) }{1 + \sin( \alpha ) } [/tex]
2. buktikan identitas trigonometri berikut.
masih di coba dulu,,
3. buktikanlah identitas trigonometri berikut
sec x = 1/cosx
csc x = 1/sinx
1+cot²x = csc²x
sinx/cosx = tan
cosx/sinx = cot
4. buktikanlah identitas trigonometri berikut:
1.
sin x (cot x + tan x)
= sin x ( cosx/sinx + sinx/cosx )
= cos x + (sin²x/cosx)
= cos²x/cosx + sin²x/cosx
= (cos²x + sin²x)/cosx = 1/cos x
b. (1+sinx)/cosx + cosx/(1+sinx)
= (1+2sinx + sin²x +cos²x)/cosx( 1+sinx)
= (2+2sinx)/cosx(1+sinx)
= 2(1+sinx)/cosx(1+sinx)
= 2/cosx
= 2 sec x
5. buktikan identitas trigonometri berikut
Materi : Identitas Trigonometri
Kelas : XI SMA
sin^2 A - sin^2 A . cos^2 A = sin^4 A
sin^2 A - sin^2 A (1 - sin^2 A ) = sin^4 A
sin^2 A - sin^2 A + sin^4 A = sin^4 A
sin^4 A = sin^4 A
TerBunKti
#Matematika_Mudah
#Smart_Logickalau ada yg kurang paham bisa ditanyakan, semoga membantu
6. buktikan identitas trigonometri berikut
Jawab:
identitas
sin² x + cos² x = 1
cos² x - sin² x = 1 - 2 sin² x
sec x = 1/cos x
csc x = 1/sin x
tan x = sin x/cos x
Penjelasan dengan langkah-langkah:
a) cos⁴ x - sin⁴ x = 1 - 2 sin² x
ruas kiri = cos⁴ x - sin⁴ x
= (cos²x + sin² x)( cos² x - sin² x)
= (1) (1 - 2 sin² x)
= 1 - 2 sin² x (terbukti )
b) cos⁴ x + sin⁴ x = 1 - 2 sin² x cos² x
ruas kiri = cos⁴ x + sin⁴ x
= (cos² x + sin² x)² - 2 sin² x cos² x
= (1)² - 2 sin² x cos² x
= 1 - 2 sin² x cos² x (terbukti)
7. buktikan identitas trigonometri berikut ini!
no 3
sin pangkat 4 A-cos pangkat 4 A
=(sin kuadrat A + cos kuadrat A)(sin kuadrat A - cos kuadrat A)
=1 - 2 cos kuadrat A
semoga membantu....
8. Buktikan identitas trigonometri berikut!
[tex] { \sec }^{4} x - { \sec }^{2} x \\ = { \sec}^{2} x( { \sec}^{2} x - 1) \\ = { \sec}^{2} x(1 + { \tan}^{2} x - 1) \\ = { \sec }^{2} ( { \tan}^{2} x) \\ = (1 + { \tan }^{2} x) { \tan }^{2} x \\ = { \tan}^{2} x + { \tan}^{4} x \\ = { { \tan }^{4} }x + { \tan }^{2} x[/tex]
Semoga jawabannya membantu.
9. buktikan identitas trigonometri berikut
semoga membantu
maaf bila keliru
10. Buktikan identitas trigonometri berikut
jawaban terlampir ya :)
