Question

Verify the identity tan^2 (x) * csc^2( x)= 1/cos^2(x)

Answer 1

We have

`\tan ^2(x)csc^2(x)=(1)/(\cos ^2(x))`
`\tan (x)=(\sin(x))/(\cos(x))`
`\csc (x)=(1)/(\sin (x))`

we substitute the equalities given above

`(\sin^2(x))/(\cos^2(x))\cdot(1^2)/(\sin^2(x))=(\sin^2(x))/(\sin^2(x)\cos^2(x))=(1)/(\cos ^2(x))`

as we can see we verify the identity because we obtain the same result