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ICSE Class 10 Answered

prove that: cosA - 2cos^3A/2sin^3A - sinA = cotA
Asked by Vru23 | 28 Jul, 2020, 08:18: PM
answered-by-expert Expert Answer
To prove: (cosA - 2cos3A)/(2sin3A - sinA) = cotA
 
LHS equals fraction numerator cosA minus 2 cos cubed straight A over denominator 2 sin cubed straight A minus sinA end fraction equals fraction numerator cosA open parentheses 1 minus 2 cos squared straight A close parentheses over denominator sinA open parentheses 2 sin squared straight A minus 1 close parentheses end fraction equals fraction numerator cosA space open parentheses negative cos 2 straight A close parentheses over denominator sinA space open parentheses negative cos 2 straight A close parentheses end fraction space space space space........ space open parentheses Since comma space cos 2 straight A equals 1 minus 2 sin squared straight A equals 2 cos squared straight A minus 1 close parentheses equals cosA over sinA equals cotA equals RHS Hence comma space fraction numerator cosA minus 2 cos cubed straight A over denominator 2 sin cubed straight A minus sinA end fraction equals cotA
Answered by Renu Varma | 29 Jul, 2020, 11:00: AM

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