ICSE Class 10 Answered
prove that: 1+cosecA+cotA=2/1+tanA-secA
![question image](http://images.topperlearning.com/topper/new-ate/top_mob159499866515925044164facc762-9aa6-4176-bb1c-a8d017a2c7b1.jpg)
Asked by saumitachaudhuri120 | 17 Jul, 2020, 20:41: PM
To prove: 1+cosecA+cotA = 2/{1+tanA-secA}
![1 plus cosecA plus cotA equals 1 plus 1 over sinA plus cosA over sinA equals fraction numerator sinA plus cosA plus 1 over denominator sinA end fraction space space... space left parenthesis 1 right parenthesis
fraction numerator 2 over denominator 1 plus tanA minus secA end fraction
equals fraction numerator 2 over denominator 1 plus begin display style sinA over cosA end style minus begin display style 1 over cosA end style end fraction
equals fraction numerator 2 over denominator begin display style fraction numerator cosA plus sinA minus 1 over denominator cosA end fraction end style end fraction
equals fraction numerator 2 cosA over denominator cosA plus sinA minus 1 end fraction
equals fraction numerator 2 cosA open parentheses cosA plus sinA plus 1 close parentheses over denominator open parentheses cosA plus sinA close parentheses squared minus 1 end fraction
equals fraction numerator 2 cosA open parentheses cosA plus sinA plus 1 close parentheses over denominator cos squared straight A plus sin squared straight A plus 2 sinAcosA minus 1 end fraction
equals fraction numerator 2 cosA open parentheses cosA plus sinA plus 1 close parentheses over denominator 2 sinAcosA end fraction
equals fraction numerator cosA plus sinA plus 1 over denominator sinA end fraction
rightwards double arrow fraction numerator 2 over denominator 1 plus tanA minus secA end fraction equals fraction numerator cosA plus sinA plus 1 over denominator sinA end fraction space space... space left parenthesis 2 right parenthesis
From space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis comma space we space have
1 plus cosecA plus cotA equals fraction numerator 2 over denominator 1 plus tanA minus secA end fraction](https://images.topperlearning.com/topper/tinymce/cache/167ee635036bc1a3f5dec959418ac2a0.png)
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