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CBSE Class 11-science Answered

ABC are angles of a triangle, Prove that sin squared fraction numerator A plus over denominator 2 end fraction sin squared B over 2 plus sin squared c over 2 equals= 1-2sinA/2*sinB/2*sinC/2
Asked by aahnik.mohanty | 20 May, 2019, 12:52: PM
answered-by-expert Expert Answer
A B C thin space a r e space a n g l e s space o f space a space t r i a n g l e space rightwards double arrow A plus B plus C equals 180 degree equals straight pi space... space left parenthesis straight i right parenthesis Consider comma space LHS equals sin squared straight A over 2 plus sin squared straight B over 2 plus sin squared straight C over 2 equals 1 half open parentheses 2 sin squared straight A over 2 plus 2 sin squared straight B over 2 plus 2 sin squared straight C over 2 close parentheses equals 1 half open parentheses 1 minus cosA plus 1 minus cosB plus 1 minus cosC close parentheses equals 1 half open parentheses 3 minus left parenthesis cosA plus cosB plus cosC right parenthesis close parentheses equals 1 half open parentheses 3 minus open parentheses 2 cos open parentheses fraction numerator straight A plus straight B over denominator 2 end fraction close parentheses cos open parentheses fraction numerator straight A minus straight B over denominator 2 end fraction close parentheses plus cosC close parentheses close parentheses equals 1 half open parentheses 3 minus open parentheses 2 cos open parentheses fraction numerator straight pi minus straight C over denominator 2 end fraction close parentheses cos open parentheses fraction numerator straight A minus straight B over denominator 2 end fraction close parentheses plus 1 minus 2 sin squared straight C over 2 close parentheses close parentheses equals 1 half open parentheses 2 minus open parentheses 2 sin straight C over 2 space cos open parentheses fraction numerator straight A minus straight B over denominator 2 end fraction close parentheses minus 2 sin squared straight C over 2 close parentheses close parentheses equals 1 half open parentheses 2 minus 2 sin straight C over 2 open parentheses cos open parentheses fraction numerator straight A minus straight B over denominator 2 end fraction close parentheses minus sin straight C over 2 close parentheses close parentheses equals 1 half open parentheses 2 minus 2 sin straight C over 2 open parentheses cos open parentheses fraction numerator straight A minus straight B over denominator 2 end fraction close parentheses minus sin fraction numerator straight pi minus left parenthesis straight A plus straight B right parenthesis over denominator 2 end fraction close parentheses close parentheses equals 1 half open parentheses 2 minus 2 sin straight C over 2 open parentheses cos open parentheses fraction numerator straight A minus straight B over denominator 2 end fraction close parentheses minus cos open parentheses fraction numerator straight A plus straight B over denominator 2 end fraction close parentheses close parentheses close parentheses equals 1 half open parentheses 2 minus 2 sin straight C over 2 open parentheses 2 sin straight A over 2 sin straight B over 2 close parentheses close parentheses equals 1 minus 2 sin straight A over 2 sin straight B over 2 sin straight C over 2
Answered by Renu Varma | 20 May, 2019, 06:13: PM

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