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Home Q & A Board Science-Related Homework Help Mathematics
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tonichilds83 tonichilds83
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11 years ago
"use properties of the trigonometric functions to find the exact value of each expression. Do not use a Calculator"

sec^2(18) - tan^2(18)
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iloveanatomyiloveanatomy
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#1
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11 years ago
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#2
11 years ago
Remember that sec^2(x) - tan^2(x) = 1 for any x. So, sec^2(18) - tan^2(18) = 1.

Hope this helps.
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#3
11 years ago
Recall that sec = 1/cos, tan = sin/cos. So we can rewrite the problem as:

1 / cos^2(18)     -     sin^2(18) / cos^2(18)

Pulling the 1/cos^2 out, we get:

(1 - sin^2(18) ) / cos^2(18)

It is a known trig property that:
cos^2(x) + sin^2(x) = 1. This implies cos^2(x) = 1 - sin^2(x)

So this simplifies to cos^2(18) / cos^2(18) = 1.
wrote...
#4
11 years ago
Use identity 1+tan^2(x) = sec^2(x)

sec^2(18) - tan^2(18)
=1+tan^2(18) - tan^2(18)
=1
wrote...
#5
11 years ago
since sec=1/cos and tan=sin/cos
sec^(18)-tan^2(18)=1/cos^2 18 -sin^2 18/cos^2 18
=1-sin^2 18/cos^2 18    ...... 1-sin^2=cos^2
=cos^2 18/cos^2 18 = 1
wrote...
#6
11 years ago
Remember that! sec^2 x = tan^2 x + 1 so

sec^2 (18) - tan^2 (18) =
tan^2 (18) + 1 - tan^2 (18) = 1
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