# Thread: How can I verify the identity when it doesn't match?

1. ## How can I verify the identity when it doesn't match?

The questions is
Verify the identity: sec(x+y)=secxsecy/1-tanxtany

I have a list of identities but it doesn't fully match either of them. Since sec is the reciprocal of sin, can I used this: sin(x-y)=sinxcosy-cosxsiny? If so, what would take the place of cos? csc? Thanks

2. Originally Posted by captaintoast87

Since sec is the reciprocal of sin
... of cos.

3. Originally Posted by Krizalid
... of cos.
...of course !

4. Hello, captaintoast87!

Verify the identity: .$\displaystyle \sec(x+y) \:=\:\frac{\sec x\sec y}{1-\tan x\tan y}$

The right side is: .$\displaystyle \frac{\dfrac{1}{\cos x}\cdot\dfrac{1}{\cos y}} {1 - \dfrac{\sin x}{\cos x}\cdot\dfrac{\sin y}{\cos y}}$

Multiply top and bottom by $\displaystyle \cos x\cos y$

. . $\displaystyle \frac{\cos x\cos y\left(\dfrac{1}{\cos x}\cdot\dfrac{1}{\cos y}\right)} {\cos x\cos y\left(1 - \dfrac{\sin x}{\cos x}\cdot\dfrac{\sin y}{\cos y}\right)} \;=\;\frac{1}{\underbrace{\cos x\cos y - \sin x\sin y}_{\text{This is }\cos(x+y)}}$ .$\displaystyle = \;\frac{1}{\cos(x+y)} \;=\;\sec(x+y)$