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Last updated at Feb. 13, 2020 by Teachoo
Transcript
Ex 3.3, 6 Prove that: cos (Ο/4βπ₯) cos (Ο/4βπ¦) β sin (Ο/4βπ₯) sin (Ο/4βπ¦) = sinβ‘(π₯ + π¦) Taking L.H.S We know that cos (A + B) = cos A cos B β sin A sin B The equation given in Question is of this form Where A = (π/4 βπ₯) B = (π/4 βπ¦) Hence cos (Ο/4βπ₯) cos (Ο/4βπ¦) β sin (Ο/4βπ₯) sin (Ο/4βπ¦) = cos [(Ο/4βπ₯)" " +(Ο/4 βπ¦)] = cos [Ο/4βπ₯+Ο/4 βπ¦] = cos [Ο/4+Ο/4βπ₯βπ¦] = cos [Ο/4+Ο/4βπ₯βπ¦] = cos [Ο/2 " " β(π₯+π¦)] Putting Ο = 180Β° = cos [(180Β°)/2β(π₯+π¦)] = cos [90Β° β(π₯+π¦)] = sin (π₯+π¦) = R.H.S Hence proved
(x + y) formula
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