Question

prove that sec theta + tan theta = cos theta/ 1 - sin theta​

Answer 1

L.H.S= secΘ + tan Θ

R.H.S= cosΘ/ 1- sin Θ

taking R.H.S= cosΘ/ 1- sinΘ

multiplying numerator and denominator by (1+ sinΘ)

cosΘ (1+ sinΘ)/ (1- sinΘ) (1 + sinΘ)

cosΘ + cosΘsinΘ / 1 - sin^2Θ

cosΘ + cosΘsinΘ / cos^2 Θ

i.e. cosΘ/ cos^2 + cosΘsinΘ/ cos^2Θ

=> 1 / cosΘ + sinΘ / cosΘ

= secΘ = tan Θ = L.H.S