cos square (60-x) +cos square (60+x) belongs to

Asked by bandlapravalika4 | 25th Sep, 2020, 01:32: PM

Expert Answer:

cos2(60 - x) - cos2(60 + x)
= [cos60 cosx + sin60 sinx]2 - [cos60 sinx - sin60 sinx]2
equals open square brackets 1 half cosx plus fraction numerator square root of 3 over denominator 2 end fraction sinx close square brackets squared minus open square brackets 1 half cosx minus fraction numerator square root of 3 over denominator 2 end fraction sinx close square brackets squared
equals fraction numerator cos squared straight x over denominator 4 end fraction plus 3 over 4 sin squared straight x plus fraction numerator square root of 3 over denominator 2 end fraction space cosx space sinx space minus space open square brackets fraction numerator cos squared straight x over denominator 4 end fraction plus 3 over 4 sin squared straight x minus fraction numerator square root of 3 over denominator 2 end fraction space cosx space sinx close square brackets
equals square root of 3 space cosx space sinx
equals space fraction numerator square root of 3 over denominator 2 end fraction space sin 2 straight x
We space know space that space minus 1 less or equal than sinx less or equal than 1 comma space straight x element of straight R
rightwards double arrow negative 1 less or equal than sin 2 straight x less or equal than 1 comma space 2 straight x element of straight R
minus fraction numerator square root of 3 over denominator 2 end fraction less or equal than fraction numerator square root of 3 over denominator 2 end fraction space sin 2 straight x less or equal than fraction numerator square root of 3 over denominator 2 end fraction
rightwards double arrow space sin 2 straight x element of open square brackets negative fraction numerator square root of 3 over denominator 2 end fraction comma space fraction numerator square root of 3 over denominator 2 end fraction close square brackets
rightwards double arrow space cos squared open parentheses 60 minus straight x close parentheses minus cos squared open parentheses 60 plus straight x close parentheses element of open square brackets negative fraction numerator square root of 3 over denominator 2 end fraction comma space fraction numerator square root of 3 over denominator 2 end fraction close square brackets 

Answered by Renu Varma | 25th Sep, 2020, 05:30: PM