Question

Is this an identity?
1+sec^2x=tan^2x

Answer 1

No, the correct identity is
`\tan^2(x)+1=\sec^2(x)`. It is obtained by dividing the both sides of the Pythagorean Trigonometric Identity by cos²(x):


`\sin^2(x)+\cos^2(x)=1\\\\ (\sin^2(x)+\cos^2(x))/(\cos^2(x))=(1)/(\cos^2(x))\\\\ (\sin^2(x))/(\cos^2(x))+(\cos^2(x))/(\cos^2(x))=(1)/(\cos^2(x))\\\\ \boxed{\tan^2(x)+1=\sec^2(x)}~~\blacksquare`