Question

Solve the equation
sin (x° - 20°) = cos 42° for x, where 0 < x <90

Answer 1

cos(90° - x + 20°) = cos 42°
110° - x = 42° => x = 110° - 42° => x = 68°

Answer 2

Value of x is 68°

Explanation:

Given: sin ( x - 20 )° = cos 42°

To find: Value of x.

We know that cos ( 90 - x )° = sin x°

So, cos 42° = cos ( 90 - 48 )° = sin 48°

Now Consider,

sin ( x - 20 )° = cos 42°

from above

sin ( x - 20 )° = sin 48°

Since both trigonometric ratios are same. ⇒ Angle must be equal.

⇒ x - 20 = 48

x = 48 + 20

x = 68

68 ∈ ( 0 , 90 )

Therefore, Value of x is 68°