Question

Find all solutions to the equation (sinx-cosx)^2=3

Answer 1

This equation has no solution.

Explanation:

We have given the equation:

(sinx-cosx)²= 3

We have to solve it.

(sinx-cosx)²= 3

sin²x+cos²x-2sinxcosx = 3

As we know that :

sin²x+cos²x = 1

so, (1)-2sinxcosx = 3

1-2sinxcosx = 3

1-sin2x = 3

sin2x=1-3

sin2x = -2

2x = sin⁻¹(-2)

The value of sinx cannot be less than -1 so, this equation has no solution.

Answer 2

no solutions

Explanation:

Simplify the equation
`(\sin x-\cos x)^2=3:`

`\sin^2 x-2\sin x\cos x+\cos ^2x=3,\\ \\ (\sin^2x+\cos^2x)-2\sin x\cos x=3.\\`

Since

`\sin^2 x+\cos^2 x=1`

and

`2\sin x\cos x=\sin 2x,`

we have

`1-\sin 2x=3,\\ \\\sin 2x=-2.`

Since
`\sin 2x` cannot be less than
`-1,` this equation has no solutions.