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

## Answer This Question

## Related Questions

- Calculus - I wanted to confirm that I solved these problems correctly (we had to...
- trig - If sin theta is equal to 5/13 and theta is an angle in quadrant II find ...
- Trigonometry - Prove the following identities: 1. (tan theta - sin theta)^2 + (1...
- Trigonometry - Prove the following identities: 1. (tan theta - sin theta)^2 + (1...
- math - I have a question I have been working on since yesterday and I am not ...
- math (trig) - if cos 2 theta = -(1/3) and theta is in Quadrant 2, find sin theta...
- Algebra II - Multiple Choice (theta) means the symbol 0 with the dash in it. 1.)...
- Math Trig Help - sin theta = x/3, with theta in the first quadrant, find the ...
- precalc h - sin(theta)/1-cos(theta) + 1-cos(theta)/sin(theta) = 2csc(theta) That...
- Trigonometry - Thank you STEVE!!!!! Suppose that Cos (theta) = 1/square root 2 ...

More Related Questions