prove that sin theta - cos theta + 1 / sin theta + cos theta - 1 = secant theta + tan theta
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Step-by-step explanation:
let theta be x
=>(sinx-cosx+1)/sinx+cosx-1
=>rationalize the denominator
(sinx-cosx+1)(sinx+cosx+1)
(sinx+cosx+1)(sinx+cosx+1)
=>sin²x+cos²x=1
sin²x+2sinx+sin²x+cos²x-cos²x
2sinxcosx
=>(sinx+1)/cosx
=>(sinx/cosx)+(1/cosx)
=>tanx+secx
i hope it's helpful
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