Question

how do I simiplify tan(x)^2=sin(x)^2/cos(x)^2 using the expression sin(x)^2+cos(x)^2=1?

Answer 1

You can solve for sin(x)^2 in the second equation. Then substitute into the first equation.

Answer 2

i dont get it :(

Answer 3

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

Answer 4

solve for sin(x)^2

Answer 5

That means get sin(x)^2 by itself on one side of the equation.

Answer 6

Isolate it!

Answer 7

i got 1-cos(x)^2

Answer 8

correct. now substitute what you got for sin(x)^2 in the first equation

Answer 9

substitute means replace sin(x)^2 with what you got.

Answer 10

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

Answer 11

now simplify the right hand side.

Answer 12

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

Answer 13

simplify further to get (1/cos(x)^2) - 1 = sec(x)^2 - 1

Answer 14

we now have tan(x)^2 = sec(x)^2 -1
add 1 to both sides of the equation to get the identity we seek.

Answer 15

Good going cebroski. But confirm in between whether the user is getting your points or not!

Answer 16

thank you mathslover

Answer 17

subodha, how are you doing?

Answer 18

i dont get how u got 1-cos(x)^2/cos(x)^2 to sec(x)^2-1 :(

Answer 19

Great question! We can distribute the denominator and split the fraction into two fractions.

Answer 20

A simpler example of this idea is (a - b)/c = a/c - b/c
Or, (2 - 1)/3 = 2/3 - 1/3

Answer 21

think of cos(x)^2 as a single object or thing. In your mind, replace it with a symbol, such as an X. 1-cos(x)^2/cos(x)^2 = (1 - X)/X = 1/X - X/X

Answer 22

1-cos(x)^2/cos(x)^2 should have parentheses around the numerator.

Answer 23

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

Answer 24

how are you doing @subodha ?

Answer 25

i think i get it
thank you :)

Answer 26

what is your final answer?

Answer 27

did you end up getting an identity with tangent and secant in it?

Answer 28

yeah
is it becuse 1/cos(x)^2 -1 is equal to sec(x)^2-1

Answer 29

i get how u got 1-cos(x)^2/cos(x)^2 to sec(x)^2-1

Answer 30

super. If you add 1 to both sides of the equation, you will get another common pythagorean trigonometric identity.

Answer 31

oh okay
thanks for helping <3