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Asked by sourabh7jain 16th June 2016, 5:17 PM
Answered by Expert
Answer:
begin mathsize 12px style cos to the power of negative 1 end exponent open parentheses cosx close parentheses equals straight x space for all straight x element of open square brackets straight pi over 2 comma space straight pi close square brackets
So space the space equation space becomes
square root of 1 plus cos 2 straight x end root equals square root of 2 cos to the power of negative 1 end exponent open parentheses cosx close parentheses
rightwards double arrow square root of 1 plus cos 2 straight x end root equals square root of 2 straight x
rightwards double arrow square root of 2 cos squared straight x end root equals square root of 2 straight x
rightwards double arrow square root of 2 square root of cos squared straight x end root equals square root of 2 straight x
rightwards double arrow square root of cos squared straight x end root equals straight x
cosx space is space negative space when space straight x element of open square brackets straight pi over 2 comma space straight pi close square brackets
So space square root of cos squared straight x end root equals negative cosx
So space the space equation space becomes space
minus cosx equals straight x
rightwards double arrow cosx equals negative straight x end style
 
begin mathsize 12px style bold The bold space bold graphs bold space bold of bold space bold cosx bold space bold and bold space bold minus bold x bold space bold do bold space bold not bold space bold have bold space bold any bold space bold points bold space bold of bold space bold intersection
bold in bold space bold the bold space bold interval bold space open parentheses bold pi over bold 2 bold comma bold pi close parentheses
bold As bold space bold shown bold space bold in bold space bold the bold space bold graph bold comma bold space bold the bold space bold maximum bold space bold value bold space bold cos bold space bold x bold space bold can bold space bold take bold space bold in bold space bold that bold space bold interval bold space bold is bold space bold minus bold 1 bold.
bold And bold space bold for bold space bold x bold equals bold pi bold comma bold space bold y bold equals bold minus bold pi bold space bold on bold space bold the bold space bold straight bold space bold line bold space bold y bold equals bold minus bold x bold.
bold So bold space bold the bold space bold graphs bold space bold do bold space bold not bold space bold intersect bold.
bold So bold space bold zero bold space bold number bold space bold of bold space bold solutions bold space bold for bold space bold the bold space bold given bold space bold equation bold space bold in bold space bold the bold space bold given bold space bold interval bold.
bold Option bold space bold A bold space bold is bold space bold correct bold. end style
Answered by Expert 17th June 2016, 10:14 AM
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