Question

Solve the question ​

Answer 1

⭐Solution ⭐

➡given here

cosx + sinx = √2 cos x .....(1)

➡Find here ,

cos x - sinx = ❓.

Now,

squaring both sides of (1),

we get,

( cos²x + sin²x +2cis x sinx )= 2cos²x

=> (1+sin2x )= 2cos²x

=> sin2x = 2cos²x-1.....(2)

Again,

(cosx-sinx)²=(cos²x+sin²x-2sinx cosx)

= (1-sin2x)

keep value by(2),

(cosx - sinx )²=(1-2cos²x+1)

= 2(1-cos²x)

= 2sin²x

so,

(cosx - sinx )= √(2sin²x)

= √2(sinx).

✨Thats proved .

✔Hopes its help's u

➡Marks Brainliest.