(tan 60 + 1 / tan 60 - 1 )^2 = 1 + cos 30 / 1 - cos 30

Asked by indirasolanki5661.9sdatl | 8th Mar, 2021, 07:37: PM

Expert Answer:

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
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
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
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

Answered by Renu Varma | 9th Mar, 2021, 08:03: PM