Sin (3x+19) = Cos (5x-25)

What is the value of x?

A) 6

B) 12

C) 18

D) 24

B

Step-by-step explanation:

Using the cofunction identity

sin x = cos (90 - x)

Given

sin (3x + 19) = cos (5x - 25), then

3x + 19 = 90 - (5x - 25)

3x + 19 = 90 - 5x + 25

3x + 19 = 115 - 5x (add 5x to both sides)

8x + 19 = 115 (subtract 19 from both sides)

8x = 96 (divide both sides by 8)

x = 12 → B

12 B

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