Question

Solve the equation sin (x° - 20°) = cos 42° for x, where 0 < x < 90. A. 62 B. 22 C. 68 D. 28

Answer 1

Find out the value of x.

To prove

As given

sin (x - 20°) = cos 42°

Now using the property .

cos y = sin (90 - y )

Thus

sin (x - 20°) = sin (90° - 42°)

x - 20° = 48°

x = 48° + 20°

x = 68°

Therefore the value of x is 68° .

Option (D) is correct.

Answer 2

sin ( x - 20° ) = cos 42°
sin ( x - 20° ) = sin ( 90° - 42° )
sin ( x - 20° ) = sin 48°
x - 20° = 48°
x = 48° + 20°
x = 68°
Answer: C ) 68°