tan^2 x + 1= sec^2 x

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

Replacing ` 1/cos x` for `sec x` , yields:

`tan^2 x + 1 = 1/(cos^2 x)`

You also may replace `sin^2 x + cos^2 x` for `1` , such that:

`tan^2 x + 1 = (sin^2 x + cos^2 x)/(cos^2 x)`

You need to replace `sin x/cos x` for `tan x` , such that:

`(sin^2 x)/(cos^2 x) + 1 = (sin^2 x + cos^2)/(cos^2 x)`

Bringing the terms to a common denominator yields:

`(sin^2 x + cos^2 x)/(cos^2 x) = (sin^2 x + cos^2)/(cos^2 x)` valid

Hence, testing if the `tan^2 x + 1= sec^2 x` holds yields that it is a valid statement.

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pramodpandey | College Teacher | (Level 3) Valedictorian

Posted on

`tan(x)=sin(x)/cos(x)`

`cos(x)=1/sec(x)`

`sec(x)=1/cos(x)`

`tan^2(x)+1=(sin(x)/cos(x))^2+1`

`=(sin^2(x))/(cos^2(x))+1`

` `

` ` `=(sin^2(x)+cos^2(x))/(cos^2(x))`

`=1/(cos^2(x))`

`=sec^2(x)`

`(sin^2(x)+cos^2(x)=1)`

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