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 }
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Question 1063075: From using trigonometric identity sinē Θ + cosē Θ = , obtain the following other pythagorean identities of + tanē Θ = secē Θ and also + cotē Θ = cscē Θ.
Thanks.
Found 2 solutions by Alan3354, rothauserc:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
From using trigonometric identity sinē Θ + cosē Θ = , obtain the following other pythagorean identities of + tanē Θ = secē Θ and also + cotē Θ = cscē Θ.
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sin^2 + cos^2 = 1
Divide by cos^2
---> tan^2 + 1 = sec^2
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sin^2 + cos^2 = 1
Divide by sin^2
Answer by rothauserc(4718) (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
:
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