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" 15.(a) "sin m((pi)/(2)+x)+cos n((pi)/(...

" 15.(a) "sin m((pi)/(2)+x)+cos n((pi)/(2)-x)

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The value of cos y cos ((pi)/(2) - x) - cos ((pi)/(2) - y) cos x + sin y cos ((pi)/(2) - x) + cos x sin ((pi)/(2) - y) is zero if

[sin ((pi) / (2) -x) + sin (pi-x)] ^ (2) + [(cos ((3 pi) / (2) -x) + cos (2 pi-x)] ^ (2) =

(cos (pi + x) cos (-x)) / (sin (pi-x) cos ((pi) / (2) -x)) = cot ^ (2) x

(cos (pi +x) cos (-x))/( sin (pi -x) cos ((pi )/(2) + x))= cot ^(2) x

(cos (pi +x) cos (-x))/( sin (pi -x) cos ((pi )/(2) + x))= cot ^(2) x

(cos (pi +x) cos (-x))/( sin (pi -x) cos ((pi )/(2) + x))= cot ^(2) x

(cos (pi +x) cos (-x))/( sin (pi -x) cos ((pi )/(2) + x))= cot ^(2) x

(cos (pi +x) cos (-x))/( sin (pi -x) cos ((pi )/(2) + x))= cot ^(2) x

(sin (pi + x) cos ((pi) / (2) + x) tan ((3 pi) / (2) -x) cot (2 pi-x)) / (sin (2 pi-x) cos (2 pi + x) csc (-x) sin ((3 pi) / (2) -x)) = 1