Jika sin x + cos x = a, maka sin⁴x + cos⁴x = . . . .tolong dijawab, harap jangan ngibul,,.... Question from @LindaMuchtar

AKRikza

Penjelasan dengan langkah-langkah:

sin x + cos x = a => Anggap sin x = x dan cos x = y

(x + y)² = a² Rumus identitas => sin²x + cos²x = 1, jadi

x² + y² + 2xy = a² x² + y² = 1

1 + 2xy = a²

2xy = a² - 1

xy = $\frac{a^{2} - 1}{2}$ => (sin x)(cos x) = $\frac{a^{2} - 1}{2}$

=>x⁴ + y⁴

=(x²)² + (y²)²

=(x²+y²)²–2x²y²

=(x²+y²)²—( $\sqrt{2}$ xy)²

=(x² + $\sqrt{2}$ xy + y²)(x² - $\sqrt{2}$ xy + y²)

= (x² + y² + $\sqrt{2}$ xy) (x² + y² - $\sqrt{2}$ xy)

= ( $1 + \sqrt{2}(\frac{a^{2} - 1}{2})$ ) ( $1 - \sqrt{2}(\frac{a^{2} - 1}{2})$ )

= $1^{2} - [\sqrt{2}(\frac{a^{2} - 1}{2})]^{2}$

= $1 - [(2^{1/2})^{2}(\frac{a^{2} - 1}{2})^{2}]$

= $1 - [2(\frac{a^{4} - 2a^{2} + 1}{4})]$

= $1 - (\frac{a^{4} - 2a^{2} + 1}{2})$

= $\frac{2}{2} - (\frac{a^{4} - 2a^{2} + 1}{2})$

= $\frac{2-(a^{4} - 2a^{2} + 1)}{2}$

= $\frac{2-a^{4} + 2a^{2} - 1}{2}$

= $\frac{-a^{4} + 2a^{2} + 1}{2} = - (\frac{a^{4} - 2a^{2} - 1}{2} )$

Semoga Membantu $\star\bigstar\boxed{\boxed{\bold{Selamat~Belajar}}}\bigstar\star$ Semoga Bermanfaat

2 votes Thanks 3

Milieth

//konsepnya

misal

a²+b² = a²+b²

a²+b²+2ab = a²+b²+2ab

a²+b²+2ab = (a+b)²

a²+b² = (a+b)²-2ab

maka

a²+b² = (a+b)²-2ab //

misal sinx = x

misal cosx = y

x+y = a

(x+y)² = a²

x²+2xy+y² = a²

2xy = a²-x²-y²

xy = a²-x²-y²/2

x⁴+y⁴ = (x²)²+(y²)²

= (x²+y²)²-2x²y²

= ((x+y)²-2xy)²-2(xy)²

= ((x+y)²-2(a²-x²-y²/2))²-2(a²-x²-y²/2)²

= ((sinx+cosx)²-2(a²-sin²x-cos²x/2))²-2(a²-sin²x-cos²x/2)²

= (a²-2(a²-(sin²x+cos²x)/2))²-2(a²-(sin²x+cos²x)/2)²

= (a²-1(a²-1))²-2(a²-(1)/2)²

= (a²-a²+1)²-2(a²-1/2)²

= 1-2(a²-1)²/4

= 1-2/4(a²-1)²

= 1-1/2(a²-1)²

= 1-1/2(a⁴-2a²+1)

= 1-1/2a⁴+a²-1/2

= -1/2a⁴+a²+1/2

1 votes Thanks 2

LindaMuchtar hasilnya yang suku kedua a² bukan? kan dari 2a²/2,, :/

Milieth iya ka, salah ketik tadi

LindaMuchtar okkay,

LindaMuchtar maaci,,

Tolong dong bagi yang bisa,, beserta cara penyelesaiannya,,

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Tolong dijawab nomor 4 yang a sampe c ya,,yang niat jawab asal-asal harap mundur teratur, ntar jawaban kalian juga bakal dihapus sama moderator,,

Tolong dijawab ya bagi yang bisa,,

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