francistcyr03 francistcyr03
  • 22-03-2021
  • Mathematics
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(sin^2x+tan^2x+cos^2x)/(sec^2x) What trig identities are used in solving this as well.

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LammettHash
LammettHash LammettHash
  • 22-03-2021

The main one is the Pythagorean identity,

sin²(x) + cos²(x) = 1

By dividing both sides by cos²(x), you get the tan-sec variant:

sin²(x)/cos²(x) + cos²(x)/cos²(x) = 1/cos²(x)

tan²(x) + 1 = sec²(x)

since tan(x) = sin(x)/cos(x) and sec(x) = 1/cos(x).

So the given expression reduces to

(sin²(x) + tan²(x) + cos²(x)) / sec²(x)

= (1 + tan²(x)) / sec²(x)

= sec²(x) / sec²(x)

= 1

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