question number 32

Asked by fk0391851 | 22nd Dec, 2020, 11:10: AM

Expert Answer:

Question: If sin theta = 3/4 prove that sqrt{(cosec2theta - cot2theta)/(sec2theta - 1)} = sqrt{7}/3
Solution:
As space sinθ equals 3 over 4 rightwards double arrow cosθ equals square root of 1 minus sin squared straight theta end root equals square root of 1 minus 9 over 16 end root equals fraction numerator square root of 7 over denominator 4 end fraction
rightwards double arrow secθ equals fraction numerator 4 over denominator square root of 7 end fraction
Also comma space cosecθ equals 4 over 3 space and space cotθ equals cosθ over sinθ equals fraction numerator square root of 7 over denominator 3 end fraction
Now comma space consider space the space LHS
square root of fraction numerator cosec squared straight theta minus cot squared straight theta over denominator sec squared straight theta minus 1 end fraction end root equals square root of fraction numerator begin display style 16 over 9 end style minus begin display style 7 over 9 end style over denominator begin display style 16 over 7 end style minus 1 end fraction end root equals square root of fraction numerator begin display style 9 over 9 end style over denominator begin display style 9 over 7 end style end fraction end root equals fraction numerator square root of 7 over denominator 3 end fraction
Hence comma space square root of fraction numerator cosec squared straight theta minus cot squared straight theta over denominator sec squared straight theta minus 1 end fraction end root equals fraction numerator square root of 7 over denominator 3 end fraction

Answered by Renu Varma | 22nd Dec, 2020, 11:27: AM