5) Which value of x satisfies the equation: sin (3x + 5)° = cos (4x + 1)º? A) 12 B):30 C)4 D) 24

Question

asked Nov 23, 2023 201k views

1 Answer

Machycek · Answer 1 · 2023-11-27T16:07:06+0000

Starting with the equation:

$\sin (3x+5)=\cos (4x+1)$

Remember the following property:

$\cos (90-A)=\sin (A)$

Then:

$\sin (89-4x)=\sin (90-4x-1)=\cos (4x+1)$

Then, the given equation translates to:

$\sin (3x+5)=\sin (89-4x)$

Then:

Solve for x:

$\begin{gathered} \Rightarrow3x+4x=89-5 \\ \Rightarrow7x=84 \\ \Rightarrow x=(84)/(7) \\ \Rightarrow x=12 \end{gathered}$

Therefore, the value of x that satisfies the equation, is: