Saturday, January 24, 2009

Prove that tan2(x) + 1 = sec2(x)

Prove that tan2(x) + 1 = sec2(x)

We know that

sin2(x) + cos2(x) = 1

dividing both sides by cos2(x) we get

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

which equals

sin2(x)/cos2(x) + cos2(x)/cos2(x) = (1/cos(x))2

which can be re-written as

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

We know that tan2(x) = (sin(x)/(cos(x))2

and that (1/cos(x))2 = sec2(x)

So we can write

cot2(x) + 1 = sec2(x)


John Tran said...

there is a typo at the end you meant to say tan not cot

Leslie Lim said...

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