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 | 13th Sep, 2014, 10:13: PM

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.
 
Thanks for asking us a question in Ask the Expert section of TopperLearning.com.
 

We cannot entertain more than 5 questions in a subject per day. In case of multiple questions within a query, please post each question individually and let us know where you are getting stuck so that we would be able to explain things better.

Regards

Topperlearning Team.

Answered by Mili Hariyani | 14th Sep, 2014, 02:27: AM