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ICSE - X - Mathematics - Matrices

if A=open square brackets table row cell tan theta end cell cell c o t theta end cell row cell negative tan theta end cell cell negative c o t theta end cell end table close square brackets and B=open square brackets table row cell tan theta end cell cell c o t theta end cell row cell fraction numerator 1 over denominator c o t theta end fraction end cell cell fraction numerator 1 over denominator tan theta end fraction end cell end table close square brackets, find AB.

Asked by savi1405 28th April 2016, 5:16 PM
Answered by Expert

Answer:

begin mathsize 12px style straight A equals open square brackets table row tanθ cotθ row cell negative tanθ end cell cell negative cotθ end cell end table close square brackets space space and space straight B equals open square brackets table row tanθ cotθ row cell 1 over cotθ end cell cell 1 over tanθ end cell end table close square brackets
AB equals open square brackets table row tanθ cotθ row cell negative tanθ end cell cell negative cotθ end cell end table close square brackets open square brackets table row tanθ cotθ row cell 1 over cotθ end cell cell 1 over tanθ end cell end table close square brackets equals open square brackets table row cell tan squared straight theta plus 1 space space space space space space space space end cell cell tanθcotθ plus cotθ over tanθ end cell row cell negative tan squared straight theta minus 1 space end cell cell negative tanθcotθ minus cotθ over tanθ end cell end table close square brackets
space space space space space space equals open square brackets table row cell sec squared straight theta space space space space space space space space end cell cell 1 plus fraction numerator cos squared straight theta over denominator sin squared straight theta end fraction end cell row cell negative sec squared straight theta space end cell cell negative 1 minus fraction numerator cos squared straight theta over denominator sin squared straight theta end fraction end cell end table close square brackets equals open square brackets table row cell sec squared straight theta space space space space space space space space end cell cell fraction numerator sin squared straight theta plus cos squared straight theta over denominator sin squared straight theta end fraction end cell row cell negative sec squared straight theta space end cell cell fraction numerator negative sin squared straight theta minus cos squared straight theta over denominator sin squared straight theta end fraction end cell end table close square brackets
space space space space space space equals open square brackets table row cell sec squared straight theta space space space space space space space space end cell cell fraction numerator 1 minus cos squared straight theta plus cos squared straight theta over denominator sin squared straight theta end fraction end cell row cell negative sec squared straight theta space end cell cell fraction numerator negative 1 plus cos squared straight theta minus cos squared straight theta over denominator sin squared straight theta end fraction end cell end table close square brackets space equals open square brackets table row cell sec squared straight theta space space space space space space space space end cell cell fraction numerator 1 over denominator sin squared straight theta end fraction end cell row cell negative sec squared straight theta space end cell cell fraction numerator negative 1 over denominator sin squared straight theta end fraction end cell end table close square brackets
space space space space space equals open square brackets table row cell sec squared straight theta space space space space space space space space end cell cell cosec squared straight theta end cell row cell negative sec squared straight theta space end cell cell negative cosec squared straight theta end cell end table close square brackets end style
Answered by Expert 29th April 2016, 8:54 AM

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