Question

prove that sin theta minus cos theta + 1 upon sin theta + cos theta minus 1 is equal to one upon sec theta minus 10 theta

Answer 1

we use identity,sec square theta =1+tan square theta
L.H.S
dividing both numerator and denominator by cos theta
we get ,
(tan theta minus 1+ sec theta )upon (tan theta + 1 - sec theta )
=( tan theta + sec theta )-1 upon (tan theta minus sec theta ) +1

multiplying and dividing by tan theta minus sec theta
= ((tan theta + sec theta )-1)(tan theta - sec theta ) upon ((tan theta - sec theta ) +1)(tan theta - sec theta )
= (tan square theta -sec square theta ) - (tan theta - sec theta) upon (tan theta - sec theta +1)(tan - sec)
= -1-tan +sec upon (tan -sec +1)(tan -sec)
-(tan - sec+1) upon (tan - sec+1)(tan - sec )
= - 1 upon (tan -sec)
= 1 upon (sec - tan ) = R.H.S


l hope it'll help u

Answer 2

★ Refer to the Attachment.