Question

1 Select the correct answer. What is the value of x? sin(4.1-10)° = cos(40-x) OA. 10 OB. r = 20 Ос. r = 50 OD 1=17

Answer 1

B. x=20

Step-by-step explanation

`\sin (4x-10)=\cos (40-x)`

by definition

`\sin (\emptyset)=\cos (90-\emptyset)`

Step 1

let

`\begin{gathered} \emptyset=4x-10 \\ 90-\emptyset=40-x \\ so \\ \sin (4x-10)=\cos (90-(4x-10)) \\ \sin (4x-10)=\cos (90-4x+10) \\ \sin (4x-10)=\cos (100-4x) \\ \text{Also} \\ \sin (4x-10)=\cos (40-x) \\ \text{hence} \\ \cos (40-x)=\cos (100-4x) \\ 40-x=100-4x \\ \text{add x in both sides} \\ 40-x+x=100-4x+x \\ 40=100-3x \\ 40-100=-3x \\ -60=-3x \\ x=(60)/(3) \\ x=20 \end{gathered}`

Let's check every option

A)

`\begin{gathered} \sin (4x-10)=\cos (40-x) \\ x=10 \\ \sin (4\cdot10-10)=\cos (40-10) \\ \sin (30)=\cos (30)\rightarrow false \end{gathered}`

B)

`\begin{gathered} \sin (4x-10)=\cos (40-x) \\ x=20 \\ \sin (4\cdot20-10)=\cos (40-20) \\ \sin (70)=\cos (20) \\ 70=90-20\rightarrow\text{true} \end{gathered}`

C)

`\begin{gathered} \sin (4x-10)=\cos (40-x) \\ x=50 \\ \sin (4\cdot50-10)=\cos (40-50) \\ \sin (190)=\cos (-10) \\ 190=90-(-10)\rightarrow\text{false} \end{gathered}`

D)

`\begin{gathered} \sin (4x-10)=\cos (40-x) \\ x=17 \\ \sin (4\cdot17-10)=\cos (40-17) \\ \sin (58)=\cos (23) \\ 58=90-23\rightarrow\text{false} \end{gathered}`

therefore, the answer is

B. x=20