1. Cos5π/4-sin5π/4+tan11π/4-cot11π/4?
  2. SIn4530°?
  3. Cos (-9π/4)?
  4. Sin 120°cos 150°-cos240°sin330°?
  5. If tan35°=k then,Tan145°-Tan125°/1+Tan145°.Tan125°?

Asked by Pallapothu.a | 5th Aug, 2020, 04:13: PM

Expert Answer:

TO find the values of given trigonometric expression
 
cos fraction numerator 5 straight pi over denominator 4 end fraction minus sin fraction numerator 5 straight pi over denominator 4 end fraction plus tan fraction numerator 11 straight pi over denominator 4 end fraction minus cot fraction numerator 11 straight pi over denominator 4 end fraction
equals cos open parentheses straight pi plus straight pi over 4 close parentheses minus sin open parentheses straight pi plus straight pi over 4 close parentheses plus tan open parentheses 3 straight pi minus straight pi over 4 close parentheses minus cot open parentheses 3 straight pi minus straight pi over 4 close parentheses
equals negative cos straight pi over 4 plus sin straight pi over 4 plus fraction numerator sin open parentheses 3 straight pi minus straight pi over 4 close parentheses over denominator cos open parentheses 3 straight pi minus straight pi over 4 close parentheses end fraction minus fraction numerator cos open parentheses 3 straight pi minus straight pi over 4 close parentheses over denominator sin open parentheses 3 straight pi minus straight pi over 4 close parentheses end fraction space space space space.... space Since space cos left parenthesis straight pi plus straight x right parenthesis equals negative cosx space and space sin left parenthesis straight pi plus straight x right parenthesis equals negative sinx
equals negative fraction numerator 1 over denominator square root of 2 end fraction plus fraction numerator 1 over denominator square root of 2 end fraction plus fraction numerator sin begin display style straight pi over 4 end style over denominator negative cos begin display style straight pi over 4 end style end fraction minus fraction numerator negative cos begin display style straight pi over 4 end style over denominator sin begin display style straight pi over 4 end style end fraction space space space..... space Since space cos left parenthesis 3 straight pi minus straight x right parenthesis equals negative cosx space and space sin left parenthesis 3 straight pi minus straight x right parenthesis equals sinx
equals 0 minus tan straight pi over 4 plus cot straight pi over 4
equals negative 1 plus 1
equals 0
Hence comma space cos fraction numerator 5 straight pi over denominator 4 end fraction minus sin fraction numerator 5 straight pi over denominator 4 end fraction plus tan fraction numerator 11 straight pi over denominator 4 end fraction minus cot fraction numerator 11 straight pi over denominator 4 end fraction equals 0
 
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Answered by Renu Varma | 6th Aug, 2020, 11:13: AM