Asked by hasanali.ali986 | 26th May, 2015, 12:11: PM

Expert Answer:

Please ask separate queries in separate posts. 
We are providing explanation for Q.No.9 here.
cos to the power of negative 1 end exponent x over a plus cos to the power of negative 1 end exponent y over b equals theta rightwards double arrow cos open parentheses cos to the power of negative 1 end exponent x over a plus cos to the power of negative 1 end exponent y over b close parentheses equals cos theta rightwards double arrow cos open parentheses cos to the power of negative 1 end exponent x over a close parentheses cos open parentheses cos to the power of negative 1 end exponent y over b close parentheses minus sin open parentheses cos to the power of negative 1 end exponent x over a close parentheses sin open parentheses cos to the power of negative 1 end exponent y over b close parentheses equals cos theta rightwards double arrow x over a cross times y over b minus fraction numerator square root of a squared minus x squared end root over denominator a end fraction fraction numerator square root of b squared minus y squared end root over denominator b end fraction equals cos theta rightwards double arrow fraction numerator x y over denominator a b end fraction minus cos theta equals fraction numerator square root of a squared minus x squared end root over denominator a end fraction fraction numerator square root of b squared minus y squared end root over denominator b end fraction S q u a r i n g space b o t h space s i d e s space w e space g e t open parentheses fraction numerator x y over denominator a b end fraction minus cos theta close parentheses squared equals fraction numerator open parentheses a squared minus x squared close parentheses open parentheses b squared minus y squared close parentheses over denominator a squared b squared end fraction rightwards double arrow fraction numerator x squared y squared over denominator a squared b squared end fraction plus cos squared theta minus 2 fraction numerator x y over denominator a b end fraction cos theta equals fraction numerator a squared b squared minus a squared y squared minus b squared x squared plus x squared y squared over denominator a squared b squared end fraction rightwards double arrow fraction numerator x squared y squared over denominator a squared b squared end fraction plus cos squared theta minus 2 fraction numerator x y over denominator a b end fraction cos theta equals 1 minus y squared over b squared minus x squared over a squared plus fraction numerator x squared y squared over denominator a squared b squared end fraction rightwards double arrow x squared over a squared minus 2 fraction numerator x y over denominator a b end fraction cos theta plus y squared over b squared equals 1 minus cos squared theta rightwards double arrow x squared over a squared minus 2 fraction numerator x y over denominator a b end fraction cos theta plus y squared over b squared equals sin squared theta

Answered by satyajit samal | 27th May, 2015, 10:36: AM