Question

cos (x°) = sin (90 - x°) Using complete sentences, explain why an infinite number of x values that will prove the trigonometric identity to be true.

Answer 1

cosx= sin(90-x)
From the RHS,
sin(90-x)= sin90cosx-cos90sinx
Since sin90=1, cos90=0
sin90cosx-cos90sinx=cosx-0=cosx (proven)

Answer 2

Explanation:

Consider the trigonometric identity:

Cos (x°) = Sin (90° - x°)

Trigonometric identity:

Sin (A - B) = Sin (A) Cos (B) - Cos (A) Sin (B)

Now, use trigonometric identity:

Cos (x°) = Sin (90° - x°) for any value of x.

Cos (x°) = Sin (90°) Cos (x°) - Cos(90°) Sin (x°)

Since, the value of sin (90°) = 1 and cos (90°) = 0.

Therefore,

Cos (x°) = 1 × Cos (x°) - 0 × Sin (x°)

Cos (x°) = Cos (x°) for any value of x.

Hence proved.