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(a)
(1)
(c) (0) :
(D)
(a)
(0)

vdots
1

rarr I
Nilai dari
cos 75^(@)-sin 16 aq

(a) $\newline$ ( $1$ ) $\newline$ (c) ( $0$ ) : $\newline$ (D) $\newline$ (a) $\newline$ ( $0$ ) $\newline$ $\vdots$ $\newline$ $1$ $\newline$ $\rightarrow I$ $\newline$ Nilai dari $\cos 75^{\circ}-\sin 16$ aq

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Simplify rational expressions

Full solution

Q. (a)

\newline

(

1

)

\newline

(c) (

0

) :

\newline

(D)

\newline

(a)

\newline

(

0

)

\newline

\vdots

\newline

1

\newline

\rightarrow I

\newline

Nilai dari

\cos 75^{\circ}-\sin 16

aq

Use Angle Sum Identity: First, let's use the exact values for $\cos(75°)$ which can be written as $\cos(45° + 30°)$ . We'll use the angle sum identity for cosine: $\cos(A + B) = \cos(A)\cos(B) - \sin(A)\sin(B)$ . $\newline$ So, $\cos(75°) = \cos(45°)\cos(30°) - \sin(45°)\sin(30°)$ .
Plug in Known Values: Now, we plug in the known values: $\cos(45°) = \sqrt{2}/2$ , $\cos(30°) = \sqrt{3}/2$ , $\sin(45°) = \sqrt{2}/2$ , and $\sin(30°) = 1/2$ . So, $\cos(75°) = (\sqrt{2}/2)(\sqrt{3}/2) - (\sqrt{2}/2)(1/2)$ .
Perform Multiplication: Let's do the multiplication: $\cos(75°) = \frac{\sqrt{6}}{4} - \frac{\sqrt{2}}{4}$ .
Simplify Expression: Now we simplify the expression: $\cos(75°) = (\sqrt{6} - \sqrt{2})/4$ .
Find $\sin(16^\circ)$ : Next, we need to find the value of $\sin(16^\circ)$ . Since we don't have an exact value for $\sin(16^\circ)$ , we'll just leave it as $\sin(16^\circ)$ .
Subtract $\sin(16°)$ : Finally, we subtract $\sin(16°)$ from $\cos(75°)$ : $(\sqrt{6} - \sqrt{2})/4 - \sin(16°)$ .

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