Trig Identities and Equations

**daviskane** · June 22nd 2007, 06:39 AM

Verifiy the following identites letting @=theta.

1. cos@= sec@ - sin@tan@

2. sin@ cos@
----- + ----- = 1
csc@ sec@

3. 1+cos@= cot@(sin@+tan@)

4. (1+cot@)^2=csc^2@+2cot@

**topsquark** · June 22nd 2007, 08:02 AM

Originally Posted by daviskane

3. 1+cos@= cot@(sin@+tan@)

You already asked the first two in a different post! Please don't double post.

3. $1 + cos(\theta) = cot(\theta)(sin(\theta) + tan(\theta))$

The RHS:
$cot(\theta)(sin(\theta) + tan(\theta))$

$= cot(\theta) \cdot sin(\theta) + 1$

$= \frac{cos(\theta)}{sin(\theta)} \cdot sin(\theta) + 1$

$= cos(\theta) + 1$
which is the LHS.

-Dan

**Soroban** · June 22nd 2007, 09:27 AM

Hello, daviskane!

Verifiy: . $4)\;(1+\cot\theta)^2\:=\:\csc^2\!\theta+2\cot\thet a$

The left side is: . $(1 + \cot\theta)^2 \:=\:1 + 2\cot\theta + \cot^2\!\theta$

. . $= \;\underbrace{(1 + \cot^2\!\theta)}_{\text{this is }\csc^2\!\theta} + \,2\cot\theta \;=\;\csc^2\!\theta + 2\cot\theta$

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