sec theta -tan theta /sec theta +tan theta =cos2 theta/(1+sin theta )2
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L.H.S.= (sec∅-tan∅)(sec∅+tan∅)/(sec∅+tan∅)
(sec∅+tan∅)
= (sec²∅-tan²∅)/(sec∅+tan∅)²
= 1/{(1/cos)+(sin∅/cos∅)}²
LCM......
= 1/{(1+sin∅)/cos∅}²
= cos²∅/(1+sin∅)²
=R.H.S.
(sec∅+tan∅)
= (sec²∅-tan²∅)/(sec∅+tan∅)²
= 1/{(1/cos)+(sin∅/cos∅)}²
LCM......
= 1/{(1+sin∅)/cos∅}²
= cos²∅/(1+sin∅)²
=R.H.S.
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Answer:hope it helps
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