Question

sin 5x cos 3x = sin 9x cos 7x​

Answer 1

Answer:

x = π/24 is the solution

Step-by-step explanation:

pls refer attachment

Answer 2

Answer:  

There are 5 solutions

Solution:

According to the Question:

Given Data:

Step 1:

$\sin (5 x) \cos (3 x)=\sin (9 x) \cos (7 x) \text { with } x \text { in }[0, \pi / 4]$

=>  

$\sin (8 x)+\sin (2 x)=\sin (16 x)+\sin (2 x)$

Step 2:

$\sin (16 x)-\sin (8 x)=0$

Step 3:

$\sin (8 x)[2 \cos (8 x)-1]=0$

Step 4:

$\sin (8 x)=0$

Calculate the value of x :

=>$\mathrm{x}=\mathrm{k} \pi / 8, \mathrm{k}=0,1,2$

=>$x=0, \pi / 8, \pi / 4$

Step 5:

Calculate the value of x :

$\cos (8 x)=1 / 2$

=>$8 \mathrm{x}=2 \mathrm{k} \pi+1-\pi / 3$

Step 6:

Result

=>$8 \mathrm{x}=/ 3,5 \mathrm{pi} / 3, \mathrm{k}=0,1(\text { reject } 2 \mathrm{pi}+\mathrm{pi} / 3)$

=>$\mathrm{x}=\pi / / 24,5 \pi / 24$