Question

It given that sin(-x) = -m where x is acute angle . express sec x in terms of m​

Answer 1

`\sec(x)=(1)/(√(1-m^2))`

Explanation:

We know that:

`\sin(-x)=-m`

First, since sine is an odd function, we can move the negative outside:

`=-\sin(x)=-m`

Divide both sides by -1:

`\sin(x)=m`

We will now use the Pythagorean Identity:

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

Substitute m for sine:

`\cos^2(x)+m^2=1`

Solve for cosine:

`\cos^2(x)=1-m^2`

Take the square root of both sides:

`\cos(x)=\pm√(1-m^2)`

Since x is an acute angle, cosine will always be positive. Thus:

`\cos(x)=√(1-m^2)`

Take the reciprocal of both sides. Hence:

`(1)/(\cos(x))=\sec(x)=(1)/(√(1-m^2))`