Trigonometry> (tan theta + sec theta -1)/(tan theta -se...

(tan theta + sec theta -1)/(tan theta -sec theta +1) = sec theta +tan theta

Nithesh , 7 Years ago

Grade 10

2 Answers

Arun

Last Activity: 7 Years ago

Dear Nithesh

Numerator = tan theta + sec theta -1
= sin theta/cos theta + 1/cos theta - 1
= (sin theta + 1)/cos theta -1

denominator = (sin theta -1)/cos theta +1

multiply both by cos theta

numerator = sin theta +1 - cos theta
= 2 sin theta/2 cos theta/2 + 2 sin^ theta/2

denominator = 2 sin theta/2 cos theta/2 - 2 sin ^2 theta/2

divide

number = (cos theta/2 + sin theta/2)/(cos theta/2 - sin theta/2)

= (cos theta/2 + sin theta/2)^2/(cos^2 theta/2- sin ^2 theta/2)
= (cos^2 theta/2+ sin^2 theta/2 + 2 cos theta/2 sin theta/2)/(cos theta)
= (1+ sin theta)/ cos theta

= sec theta+ tan theta

Hence Proved

ankit singh

Last Activity: 4 Years ago

convert all into sine and cosine then further simplify to get the result

(cos theta/2 + sin theta/2)^2/(cos^2 theta/2- sin ^2 theta/2)
= (cos^2 theta/2+ sin^2 theta/2 + 2 cos theta/2 sin theta/2)/(cos theta)
= (1+ sin theta)/ cos theta

= sec theta+ tan theta