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CBSE Class 10 Answered

prove that :
Q1) 1/cosec x-cot x -1/sin x= 1/sin x - 1/cosec x + cot x
 
Q2) cos A/1-tan A + sin A /1-cot A= cos A + sin A
 
Q3) tan^2 A - tan^2B = sin^2 A-sin^2B/cos^2 A cos^2 B
Asked by Rajeev | 13 Sep, 2014, 10:13: PM
answered-by-expert Expert Answer
Q.1. fraction numerator 1 over denominator cos e c x space minus space c o t x end fraction minus fraction numerator 1 over denominator sin x end fraction L. H. S. equals fraction numerator 1 over denominator cos e c x space minus space c o t x end fraction minus fraction numerator 1 over denominator sin x end fraction equals fraction numerator 1 over denominator cos e c x space minus space c o t x end fraction cross times fraction numerator cos e c x space plus space c o t x over denominator cos e c x space plus space c o t x end fraction minus fraction numerator 1 over denominator sin x end fraction equals fraction numerator cos e c x space plus space c o t x over denominator cos e c squared x space minus space c o t squared x end fraction minus cos e c x equals space cos e c x space plus space c o t x space minus space cos e c x equals space cos e c x space plus space left parenthesis c o t x space minus space cos e c x right parenthesis equals cos e c x space plus space fraction numerator c o t x space minus space cos e c x over denominator cos e c squared x space minus space c o t squared x end fraction space space space space space space space space space space left square bracket because cos e c squared x space minus space c o t squared x space equals space 1 right square bracket equals cos e c x space minus space fraction numerator cos e c x space minus space co t x over denominator cos e c squared x space minus space c o t squared x end fraction space equals space cos e c x space minus space fraction numerator cos e c x space minus space co t x over denominator left parenthesis cos e c x space minus space c o t x right parenthesis left parenthesis cos e c x space plus space c o t x right parenthesis end fraction equals cos e c x space minus space fraction numerator 1 over denominator left parenthesis cos e c x space plus space c o t x right parenthesis end fraction equals space fraction numerator 1 over denominator sin x end fraction space minus space fraction numerator 1 over denominator cos e c x space plus space c o t x end fraction equals space R. H. S.
 
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Answered by Mili Hariyani | 14 Sep, 2014, 02:27: AM

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