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Prove that: sec theta + tan theta = (c...

Prove that:
`sec theta + tan theta = (cos theta)/(1-sin theta)`.

Text Solution

Verified by Experts

LHS = `sec theta + tan theta ` ltbgt ` = 1/(cos theta) + sintheta/costheta`
…`(sec theta = 1/costheta, tantheta = sintheta/costheta )`
`=((1+sin theta)(1-sin theta))/(cos theta (1-sintheta))`
….[Multiplying (`1-sin theta)` with the numerator and the derominator]
`=(1^2-sin^2 theta)/(cos theta (1-sintheta))`
` = cos^2theta/(costheta(1-sin theta))`
`= costheta/(1-sintheta)`
=RHS
`therefore` LHS=RHS
`therefore sec theta + tan theta = (cos theta)/(1-sintheta)`
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