Question

1 + sec^2x sin^2x = sec^2x

Answer 1

Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation.

Answer 2

is the sec^2(x) and sin^2(x) being multiplied? @erickkoro

Answer 3

yeah , i guess @genius12

Answer 4

Ok then. This is how it will work. We will start by changing the left side to look like the right side:\[\bf L.H.S=1+\sec^2(x)\sin^2(x)=1+\frac{ 1 }{ \cos^2(x) }\sin^2(x)=1+\frac{\sin^2(x) }{ \cos^2(x) }\]Note the sin^2(x) and cos^2(x) become tan^2(x):\[\bf = 1+\tan^2(x)\]Now using the following identity:\[\bf \sec^2(x)=1+\tan^2(x)\]We know that we have proved that the left/right hand sides are equal:\[\bf \implies L.H.S=R.H.S\]
@erickkoro

Answer 5

that's it ? @genius12