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Prove that: 1/(cos(x-a)cos(x-b))=(tan(x-...

Prove that: `1/(cos(x-a)cos(x-b))=(tan(x-b)-"tan"(x-a))/(sin(a-b))`

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L.H.S
`=(tan(x-b)-"tan"(x-a))/(sin(a-b))`
`=((sin(x-b))/(cos(x-b))-(sin(x-a))/(cos(x-a)))/sin(a-b)`
`=(sin(x-b)cos(x-a)-cos(x-b)sin(x-a))/(cos(x-b)cos(x-a)sin(a-b))`
`=sin(x-b-x+a)/(cos(x-b)cos(x-a)sin(a-b))`
`=sin(a-b)/(cos(x-b)cos(x-a)sin(a-b))`
`=1/(cos(x-b)cos(x-a))`
So,L.H.S=R.H.S
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