full under root sec theta minus one upon sec theta + 1 + full under root sec theta + 1 upon sec theta minus 1 equal to cosec theta what is the correct way of doing this may you please help with explanation
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Tp prove : √secФ-1/√secФ+1 + √secФ+1/√secФ-1 = 2cosecФ
LHS⇒ (√secФ-1)² + (√secФ+1)² / √sec²Ф-1
= secФ-1 + secФ+1 / √tan²Ф
= 2secФ/tanФ
=2×1/cosФ / sinФ/cosФ
=2cosФ/sinФ×cosФ
=2/sinФ
=2cosecФ=RHS
hence proved
LHS⇒ (√secФ-1)² + (√secФ+1)² / √sec²Ф-1
= secФ-1 + secФ+1 / √tan²Ф
= 2secФ/tanФ
=2×1/cosФ / sinФ/cosФ
=2cosФ/sinФ×cosФ
=2/sinФ
=2cosecФ=RHS
hence proved
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