Question

cos x + sin x =1/✓2 ​

Answer 1

Answer:

105 degrees

Step-by-step explanation:

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Answer 2

Answer:

x = (-15°) or (-π/12)

Step-by-step explanation:

We have,

Sinx + Cosx = (1/√2)

Squaring both sides,

(Sinx + Cosx)² = (1/√2)²

Sin²x + 2SinxCosx + Cos²x = (1/2)

We know that,

Sin²x + Cos²x = 1

Then,

Sin²x + Cos²x + 2SinxCosx = (1/2)

1 + 2SinxCosx = (1/2)

2SinxCosx = (1/2) - 1

2SinxCosx = (-1/2)

But we know that,

Sin(2x) = 2SinxCosx

So,

Sin(2x) = (-1/2)

Sin^(-1)(Sin(2x)) = Sin^(-1)(-1/2)

2x = Sin^(-1) (-1/2)

2x = (-30°) or (-π/6)

x = (-30°)/2 or (-π/6)/2

x = (-15°) or (-π/12)

Hence,

x = (-15°) or (-π/12)

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