Simplify Trigonometric Expressions...4

[nycmathguy]

Section 5.1

Question 22

sin^2 x•sec^2 x - sin^2 x

sin^2 x(sec^2 x - 1)

I know that sec^2 x - 1 = tan^2 x.

sin^2 x(tan^2 x)

sin^2 x (sin^2 x/cos^2 x)

sin^4 x/cos^2 x

Is this right?

 

[MathLover1]

correct

just simplify
sin^4 (x)/cos^2( x)=sin^2(x)*tan^2(x)

 

[nycmathguy]

correct

just simplify
sin^4 (x)/cos^2( x)=sin^2(x)*tan^2(x)

I don't understand the simplification.

How does sin^4 (x)/cos^2( x)= sin^2(x)*tan^2(x)?

 

[MathLover1]

sin^4 (x)=sin^2 (x)*sin^2 (x)

then you have

which is

= sin^2(x)*tan^2(x)

 

[nycmathguy]

sin^4 (x)=sin^2 (x)*sin^2 (x)

then you have

which is

= sin^2(x)*tan^2(x)

When you break it down piece by piece, it all makes sense.