Question

What is the value of x?

sin(x+16)°=cos(2x+14)°

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Answer 1

sin(x+16)° = cos(2x+14)° => sin(x+16) = sin(90° - (2x+14)) = sin(76 - 2x).

So x+16 = 76 - 2x + 360k or x+16 = 180 - (76 - 2x) + 360k, k ∈ Z.

From the first: 3x = 60 + 360k ⇒ x = 20 + 120k.
From the second: -x = 88 + 360k ⇒ x = -88 - 360k ⇒ x = 272 + 360k (equivalently modulo 360).

All solutions: x = 20 + 120k or x = 272 + 360k, k ∈ Z.

In [0°,360°): x = 20°, 140°, 260°, 272°.