ICSE Class 10 Answered
sec A(1 -sec A)(sec A + tan A)= 1
Asked by ketakiudeshi | 13 Jul, 2019, 14:10: PM
The question should be like this
sec A(1 - sin A)(sec A + tan A) = 1
LHS = sec A(1 - sin A)(sec A + tan A)
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![begin mathsize 16px style sec space straight A open parentheses fraction numerator 1 minus sin space straight A over denominator 1 plus sin space straight A end fraction close parentheses cross times open parentheses 1 plus sin space straight A close parentheses open parentheses sec space straight A space plus thin space tan space straight A close parentheses end style](https://images.topperlearning.com/topper/tinymce/cache/d536eabeff93b3fca68614a3c6ad016a.png)
= ![begin mathsize 16px style fraction numerator 1 over denominator cos space straight A end fraction cross times fraction numerator 1 minus sin squared space straight A over denominator 1 plus sin space straight A end fraction open parentheses fraction numerator 1 over denominator cos begin display style space end style begin display style straight A end style end fraction plus fraction numerator sin begin display style space end style begin display style straight A end style over denominator cos begin display style space end style begin display style straight A end style end fraction close parentheses end style](https://images.topperlearning.com/topper/tinymce/cache/6935bd44e7fca2ec199023f7d871ca15.png)
![begin mathsize 16px style fraction numerator 1 over denominator cos space straight A end fraction cross times fraction numerator 1 minus sin squared space straight A over denominator 1 plus sin space straight A end fraction open parentheses fraction numerator 1 over denominator cos begin display style space end style begin display style straight A end style end fraction plus fraction numerator sin begin display style space end style begin display style straight A end style over denominator cos begin display style space end style begin display style straight A end style end fraction close parentheses end style](https://images.topperlearning.com/topper/tinymce/cache/6935bd44e7fca2ec199023f7d871ca15.png)
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= 1
Hence, sec A(1 - sin A)(sec A + tan A) = 1
Answered by Sneha shidid | 15 Jul, 2019, 12:55: PM
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