SOLUTION: From using trigonometric identity sinē Θ + cosē Θ = {{{ 1 }}}, obtain the following other pythagorean identities of {{{ 1 }}} + tanē Θ = secē Θ and also {{{ 1 }

Algebra ->  Test -> SOLUTION: From using trigonometric identity sinē Θ + cosē Θ = {{{ 1 }}}, obtain the following other pythagorean identities of {{{ 1 }}} + tanē Θ = secē Θ and also {{{ 1 }      Log On


   

Question 1063075: From using trigonometric identity sinē Θ + cosē Θ = +1+, obtain the following other pythagorean identities of +1+ + tanē Θ = secē Θ and also +1+ + cotē Θ = cscē Θ.
Thanks.
Found 2 solutions by Alan3354, rothauserc:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
From using trigonometric identity sinē Θ + cosē Θ = +1+, obtain the following other pythagorean identities of +1+ + tanē Θ = secē Θ and also +1+ + cotē Θ = cscē Θ.
-----------
sin^2 + cos^2 = 1
Divide by cos^2
---> tan^2 + 1 = sec^2
========================
sin^2 + cos^2 = 1
Divide by sin^2

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
1) 1 + tan^2 theta = 1 + (sin^2 theta / cos^2 theta) =
:
(cos^2 theta + sin2 theta) / cos^2 theta = 1 / cos^2 theta = sec^2 theta
:
2) 1 + cot^2 theta = 1 + (cos^2 theta / sin^2 theta) =
:
(sin^2 theta + cos^2 theta) / sin^2 theta = 1 / sin^2 theta = csc^2 theta
: