Question

Sinx - cosx =0
find the value of secx

Answer 1

`\displaystyle \sec x=\pm√(2)`

Explanation:

Trigonometric Equations

We need to recall the identity:

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

Solving for the sine:

`\sin^2 x=1-\cos ^2 \qquad\qquad [1]`

We are given the equation:

`\sin x-\cos x=0`

Or, equivalently:

`\sin x=\cos x`

Squaring:

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

Substituting from [1]

`1-\cos ^2 =\cos^2 x`

Simplifying:

`2\cos ^2=1`

Solving:

`\displaystyle \cos^2x=(1)/(2)`

`\displaystyle \cos x=\pm\sqrt{(1)/(2)}`

Since:

`\sec x = (1)/(\cos x):`

`\mathbf{\displaystyle \sec x=\pm√(2)}`