tan2 x+1=sec2 x
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calendarEducator since 2011
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You need to remember the following trigonometric identity such that:
`1 + tan^2 x = 1/(cos^2 x)`
Hence, substituting `1/(cos^2 x)` for `1 + tan^2 x` yields:
`1/(cos^2 x) = sec^2 x`
Since the definition of secant function is the following `sec x = 1/cos x` , hence, `sec^2 x = (1/ cos x)^2`
Substituting `(1/ cos x)^2` for `sec^2 x` yields:
`1/(cos^2 x) = (1/ cos x)^2 => 1/(cos^2 x) = 1/(cos^2 x)`
Since using the trigonometric identities `1 + tan^2 x = 1/(cos^2 x)` and `sec x = 1/cos x` , yields the left side equal to the right side, hence, the given identity `1 + tan^2 x = sec^2 x` holds.
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calendarEducator since 2012
write511 answers
starTop subjects are Math, Science, and Business
Use the identities `tanx = sinx/cosx` and `secx = 1/cosx`
Then `tan^2x +1 = (sinx/cosx)^2 + 1= (sin^2x)/(cos^2x) + (cos^2x)/(cos^2x)`
`= (sin^2x + cos^2x)/(cos^2x) = 1/(cos^2x)`
(using `sin^2x + cos^2x = 1`)
The proof is complete
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