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CBSE Class 11-science Answered

Evaluate : (1+cos π/8 ) (1+cos 3π/8 ) (1+cos 5π/8 ) (1+cos 7π/8 )
Asked by tps.mjmdr | 16 Jun, 2018, 05:42: PM
answered-by-expert Expert Answer
begin mathsize 16px style open parentheses 1 plus cos straight pi over 8 close parentheses open parentheses 1 plus cos fraction numerator 3 straight pi over denominator 8 end fraction close parentheses open parentheses 1 plus cos fraction numerator 5 straight pi over denominator 8 end fraction close parentheses open parentheses 1 plus cos fraction numerator 7 straight pi over denominator 8 end fraction close parentheses equals open parentheses 1 plus cos straight pi over 8 close parentheses open parentheses 1 plus cos fraction numerator 3 straight pi over denominator 8 end fraction close parentheses open parentheses 1 plus cos open parentheses straight pi minus fraction numerator 3 straight pi over denominator 8 end fraction close parentheses close parentheses open parentheses 1 plus cos open parentheses straight pi minus straight pi over 8 close parentheses close parentheses equals open parentheses 1 plus cos straight pi over 8 close parentheses open parentheses 1 plus cos fraction numerator 3 straight pi over denominator 8 end fraction close parentheses open parentheses 1 minus cos fraction numerator 3 straight pi over denominator 8 end fraction close parentheses open parentheses 1 minus cos straight pi over 8 close parentheses equals open parentheses 1 minus cos squared straight pi over 8 close parentheses open parentheses 1 minus cos squared fraction numerator 3 straight pi over denominator 8 end fraction close parentheses equals sin squared straight pi over 8 cross times open square brackets 1 minus cos squared open parentheses straight pi over 2 minus straight pi over 8 close parentheses close square brackets equals sin squared straight pi over 8 cross times cos squared straight pi over 8 equals 1 fourth cross times open parentheses 2 sin straight pi over 8 cos straight pi over 8 close parentheses open parentheses 2 sin straight pi over 8 cos straight pi over 8 close parentheses equals 1 fourth cross times sin straight pi over 4 sin straight pi over 4 equals 1 fourth cross times sin squared straight pi over 4 equals 1 fourth cross times open parentheses fraction numerator 1 over denominator square root of 2 end fraction close parentheses squared equals 1 over 8 end style
Answered by Sneha shidid | 18 Jun, 2018, 10:27: AM

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