Question

( tan ( 90°- theta) ÷ cosec theta +1 ) + ( cosec theta +1 ÷ cot theta) = 2 sec theta prove

Answer 1

tan(90 - x)/cosecx - 1 + cosecx + 1 / cotx

= cotx/cosecx + 1 + cosecx + 1 / cotx (tan(90 - x) = cotx)

= cot²x + (cosecx + 1)² / cotx(cosecx +1)

= cot²x + cosec²x + 2cosecx + 1 / cotx(cosecx + 1)

= cot²x + cosec²x + cosec²x - cot²x + 2cosecx / cotx(cosecx + 1)

(cosec²x - cot²x = 1)

= 2cosec²x + 2cosecx / cotx(cosecx + 1)

=2cosecx(cosecx + 1) / cotx(cosecx + 1)

= 2cosecx / cotx

= 2 *1/sinx / cosx / sinx

=2 * 1/cosx

= 2secx