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Given that sin (5x - 28)o = cos (3x - 50)o

Given that sin (5x - 28)o = cos (3x - 50)o,0 < x < 90o, find the value of x

A.

14o

B.

21o

C.

32o

D.

39o

View answer & explanation

Correct answer is B

Sin (5x – 28)o = cos (3x - 50)o
Since by the trigonometry relation
Sin(5x – 28)o = cos[90 – (5x – 28)]o
Hence cos(3x – 50)o = cos[90 – (5x – 28)]o
3x – 50 = 90 - (5x-28)
3x – 50 = 90 – 5x + 28
3x + 5x = 90 + 28 + 50
8x = 168
x=1688=21∘

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