Question

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

Answer 1

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:

$3x+5=89-4x$

Solve for x:

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

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

$x=12$