ICSE Class 9 Answered
(tan 60 + 1 / tan 60 - 1 )^2 = 1 + cos 30 / 1 - cos 30
Asked by indirasolanki5661.9sdatl | 08 Mar, 2021, 19:37: PM
Since, ![tan 30 equals square root of 3 space space and space space cos 30 equals fraction numerator square root of 3 over denominator 2 end fraction](https://images.topperlearning.com/topper/tinymce/cache/b93fc22fbc95ad8925d3f8183dfd717f.png)
![tan 30 equals square root of 3 space space and space space cos 30 equals fraction numerator square root of 3 over denominator 2 end fraction](https://images.topperlearning.com/topper/tinymce/cache/b93fc22fbc95ad8925d3f8183dfd717f.png)
![open parentheses fraction numerator tan space 60 plus 1 over denominator tan space 60 minus 1 end fraction close parentheses squared equals open parentheses fraction numerator square root of 3 plus 1 over denominator square root of 3 minus 1 end fraction close parentheses squared equals open parentheses fraction numerator 3 plus 1 plus 2 square root of 3 over denominator 3 minus 1 end fraction close parentheses squared equals open parentheses 2 plus square root of 3 close parentheses squared equals 4 plus 3 plus 2 square root of 3 equals 7 plus 2 square root of 3](https://images.topperlearning.com/topper/tinymce/cache/46b02d0c81861a977870bc2da8d380c9.png)
![fraction numerator 1 plus cos space 30 over denominator 1 minus cos space 30 end fraction equals fraction numerator 1 plus begin display style fraction numerator square root of 3 over denominator 2 end fraction end style over denominator 1 minus begin display style fraction numerator square root of 3 over denominator 2 end fraction end style end fraction equals fraction numerator 2 plus square root of 3 over denominator 2 minus square root of 3 end fraction equals fraction numerator 4 plus 3 plus 2 square root of 3 over denominator 4 minus 3 end fraction equals 7 plus 2 square root of 3](https://images.topperlearning.com/topper/tinymce/cache/effca8ce7f3d637a73e06de92972a46d.png)
Hence, ![open parentheses fraction numerator tan space 60 plus 1 over denominator tan space 60 minus 1 end fraction close parentheses squared equals fraction numerator 1 plus cos space 30 over denominator 1 minus cos space 30 end fraction](https://images.topperlearning.com/topper/tinymce/cache/8ad0dfe9e14c3dae8773bc90235beffa.png)
![open parentheses fraction numerator tan space 60 plus 1 over denominator tan space 60 minus 1 end fraction close parentheses squared equals fraction numerator 1 plus cos space 30 over denominator 1 minus cos space 30 end fraction](https://images.topperlearning.com/topper/tinymce/cache/8ad0dfe9e14c3dae8773bc90235beffa.png)
Answered by Renu Varma | 09 Mar, 2021, 20:03: PM
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