Question

Use the fundamental trigonometric identities to simplify the expressions. Show all steps for full credit. HELP ME PLEASE
1.sec^2 x-tan^2 x=
2.cos^2 x(1+tan^2 x)=
3.secxcos(-x)-sin^2 x=
4.sec^2 x-1 / sin^2 x=

Answer 1

first one is 1

Answer 2

second one is 1

Answer 3

the first one :

1/cos^2 -sin^2x/cos^2x= (1-sin^2x)/cos^2x= cos^2x/cos^2x=1

Answer 4

second one:

cos^2x((cos^2x + sin^2x)/cos^2x)=cos^2x *1/cos^2x=1

Answer 5

thanks. :)

Answer 6

the third one :
1/cosx * cos(x) -sin^2x = 1-sin^2x= cos^2x

Answer 7

the last one:

sec^2 x-1 / sin^2 x= (1/cos^2x -1)/sin^2x= ((1-cos^2x)/cos^2x)/sin^2x=(sin^2x/cos^2x)/sin^2x= 1/cos^2x= sec^2x

Answer 8

\(\bf sec(x)cos(-x)-sin^2(x)\\ \quad \\
\textit{check you identities}\quad cos(-x)=cos(x)\qquad sec(x)=\cfrac{1}{cos(x)}\\ \quad \\
sec(x)cos(-x)-sin^2(x)\implies
\cfrac{1}{\cancel{cos(x)}}\cdot \cancel{cos(x)}-sin^2(x)\\ \quad \\
1-sin^2(x)\implies \square ?\)

Answer 9

hope you understood sweetie!

Answer 10

i do . thanks :)