Ques:

Asked by sourabh7jain | 16th Jun, 2016, 05:25: PM

Expert Answer:

begin mathsize 12px style open vertical bar table row 0 cosθ sinθ row cosθ sinθ 0 row sinθ 0 cosθ end table close vertical bar squared equals left square bracket negative cos straight theta left parenthesis cos squared straight theta right parenthesis plus sinθ left parenthesis negative sin squared straight theta right parenthesis right square bracket squared equals left square bracket cos cubed straight theta plus sin cubed straight theta right square bracket squared
We space are space given space that space cos 2 straight theta equals 0
rightwards double arrow 2 straight theta equals left parenthesis 2 straight n plus 1 right parenthesis straight pi over 2 rightwards double arrow straight theta equals left parenthesis 2 straight n plus 1 right parenthesis straight pi over 4
If space straight n equals 0 comma space straight theta equals straight pi over 4
If space straight n equals 1 comma space straight theta equals fraction numerator 3 straight pi over denominator 4 end fraction
If space space straight theta equals straight pi over 4 comma space left square bracket cos cubed straight theta plus sin cubed straight theta right square bracket squared equals open square brackets space cos cubed open parentheses straight pi over 4 close parentheses plus sin cubed open parentheses straight pi over 4 close parentheses close square brackets squared equals open square brackets space fraction numerator 1 over denominator 2 square root of 2 end fraction plus fraction numerator 1 over denominator 2 square root of 2 end fraction close square brackets squared equals 1 half
If space space straight theta equals fraction numerator 3 straight pi over denominator 4 end fraction comma space left square bracket cos cubed straight theta plus sin cubed straight theta right square bracket squared equals open square brackets space cos cubed open parentheses fraction numerator 3 straight pi over denominator 4 end fraction close parentheses plus sin cubed open parentheses fraction numerator 3 straight pi over denominator 4 end fraction close parentheses close square brackets squared equals open square brackets negative fraction numerator 1 over denominator square root of 2 end fraction plus fraction numerator 1 over denominator square root of 2 end fraction close square brackets squared equals 0
Since space cosine space is space straight a space periodic space function comma space these space 2 space values space will space repeat space for space straight n space equals space 5 comma space 7 comma space and space so space on.
Hence comma space open vertical bar table row 0 cosθ sinθ row cosθ sinθ 0 row sinθ 0 cosθ end table close vertical bar squared equals 1 half space or space 0. end style

Answered by Rebecca Fernandes | 17th Jun, 2016, 11:04: AM