Verified answer

Answer:

(iv) [tex]\frac{1}{\sqrt{2}}[/tex]

Step-by-step explanation:

[tex]$\cos \left(\frac{-9 \pi}{4}\right)$[/tex]

Simplify

[tex]=\cos \left(-\frac{9 \pi}{4}\right)[/tex]

Use the following property: [tex]$\cos (-x)=\cos (x)$[/tex]

[tex]$$\begin{aligned}&\cos \left(-\frac{9 \pi}{4}\right)=\cos \left(\frac{9 \pi}{4}\right) \\&=\cos \left(\frac{9 \pi}{4}\right)\end{aligned}$$[/tex]

[tex]$$\begin{aligned}&\cos \left(\frac{9 \pi}{4}\right)=\cos \left(\frac{\pi}{4}\right) \\&=\cos \left(\frac{\pi}{4}\right)\end{aligned}$$[/tex]

[tex]\cos \left(\frac{\pi}{4}\right)=\frac{1}{\sqrt{2}}[/tex]

Hence, the correct option is (iv) [tex]\frac{1}{\sqrt{2}}[/tex]

Step-by-step explanation:

Answer:

(iv) \frac{1}{\sqrt{2}}

2

1

Step-by-step explanation:

\cos \left(\frac{-9 \pi}{4}\right)cos(

4

−9π

)

Simplify

=\cos \left(-\frac{9 \pi}{4}\right)=cos(−

4

9π

)

Use the following property: \cos (-x)=\cos (x)cos(−x)=cos(x)

\begin{gathered}\begin{aligned}&\cos \left(-\frac{9 \pi}{4}\right)=\cos \left(\frac{9 \pi}{4}\right) \\&=\cos \left(\frac{9 \pi}{4}\right)\end{aligned}\end{gathered}

\begin{gathered}\begin{aligned}&\cos \left(\frac{9 \pi}{4}\right)=\cos \left(\frac{\pi}{4}\right) \\&=\cos \left(\frac{\pi}{4}\right)\end{aligned}\end{gathered}

\cos \left(\frac{\pi}{4}\right)=\frac{1}{\sqrt{2}}cos(

4

π

)=

2

1

Hence, the correct option is (iv) \frac{1}{\sqrt{2}}

2

1