Archive
9th of September 2015
Mathematics
Q:

prove the following: 1 / cosec theta-cot theta - 1/ sin theta = 1 / sin theta - 1/ cosec theta + cot theta

Nisha_vini29 - CBSE - Class X

Monday, September 07, 2015 at 22:02:PM

A:

C o n s i d e r space t h e space L H S space o f space t h e space g i v e n space e q u a t i o n colon L H S equals fraction numerator 1 over denominator cos e c theta minus c o t theta end fraction minus fraction numerator 1 over denominator sin theta end fraction space space space space space space space equals fraction numerator 1 over denominator c o s e c theta minus c o t theta end fraction cross times fraction numerator c o s e c theta plus c o t theta over denominator c o s e c theta plus c o t theta end fraction minus fraction numerator 1 over denominator s i n theta end fraction space space space space space space space equals fraction numerator c o s e c theta plus c o t theta over denominator c o s e c squared theta minus c o t squared theta end fraction minus fraction numerator 1 over denominator s i n theta end fraction space space space space space space space equals fraction numerator c o s e c theta plus c o t theta over denominator 1 end fraction minus fraction numerator 1 over denominator s i n theta end fraction space space space space space space space equals fraction numerator s i n theta open parentheses cos e c theta plus c o t theta close parentheses minus 1 over denominator s i n theta end fraction space space space space space space space equals fraction numerator 1 plus cos theta minus 1 over denominator s i n theta end fraction space space space space space space space equals fraction numerator 1 over denominator s i n theta end fraction plus fraction numerator c o s theta over denominator s i n theta end fraction minus fraction numerator 1 over denominator s i n theta end fraction space space space space space space space equals fraction numerator 1 over denominator s i n theta end fraction plus c o t theta minus cos e c theta space space space space space space space equals fraction numerator 1 over denominator s i n theta end fraction minus open parentheses cos e c theta minus c o t theta close parentheses space space space space space space space equals fraction numerator 1 over denominator s i n theta end fraction minus open parentheses c o s e c theta minus c o t theta close parentheses cross times fraction numerator open parentheses c o s e c theta plus c o t theta close parentheses over denominator open parentheses c o s e c theta plus c o t theta close parentheses end fraction space space space space space space space equals fraction numerator 1 over denominator s i n theta end fraction minus fraction numerator 1 over denominator open parentheses c o s e c theta plus c o t theta close parentheses end fraction H e n c e space p r o v e d.

Wednesday, September 09, 2015 at 18:08:PM