Posted by **Chay** on Tuesday, July 24, 2012 at 11:02am.

Claim: For all theta such that

-pie/2<theta<pie/2 the following holds true:

(1+tan(theta))^2=1/cos(theta)

- Trig -
**Reiny**, Tuesday, July 24, 2012 at 11:40am
LS = (1+ tanØ)^2

= 1 + 2tanØ + tan^2 Ø

= 1 + 2tanØ + sec^2 Ø - 1

= 2sinØ/cosØ + 1/cos^2 Ø

= (2sinØcosØ + 1)/cos^2 Ø

= (sin^2 Ø + cos^2 Ø + 2sinØcosØ)/cos^2 Ø

= (sinØ + cosØ)^2 /cosØ

≠ RS

The identity is false , all we need is one example when it does not work

e.g. Ø=30°

LS = (1+tan30°)^2 = appr 2.488

RS = 1/cos30° = 1.15

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