Question

Verify the identity.

Answer 1

\[1 + \sec ^{2}xsin ^{2}x = \sec ^{2}x\]

Answer 2

\[\frac{ 1 }{ \cos^2x }=\sec^2x\]

Answer 3

is there a shorter way of explaning it.

Answer 4

\[se^2 =\frac{1}{cos^2}\\therefore1+\frac{sin^2}{cos^2}=1+tan^2=sec^2\]

Answer 5

using \[\sin^2x+\cos^2=1\]
from second step:
\[\frac{ \sin^2x }{\cos^2x }+\frac{ \cos^2x }{\cos^2x }=\frac{ 1 }{ \cos^2x }\]
\[\tan^2x+1=\sec^2x\]