Ex 3.3, 6 - Prove that cos (pi/4 - x) cos (pi/4 - y) - Chapter 3 - (x + y) formula

  1. Chapter 3 Class 11 Trigonometric Functions
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Ex 3.3, 6 Prove that: cos (Ο€/4βˆ’π‘₯) cos (Ο€/4βˆ’π‘¦) – sin (Ο€/4βˆ’π‘₯) sin (Ο€/4βˆ’π‘¦) = sin⁑(π‘₯ + 𝑦) Taking L.H.S We know that cos (A + B) = cos A cos B – sin A sin B The equation given in Question is of this form Hence A = ( πœ‹/4 βˆ’π‘₯) B = ( πœ‹/4 βˆ’π‘¦) Hence cos (Ο€/4βˆ’π‘₯) cos (Ο€/4βˆ’π‘¦) – sin (Ο€/4βˆ’π‘₯) sin (Ο€/4βˆ’π‘¦) = cos [(Ο€/4βˆ’π‘₯)" " +(Ο€/4 βˆ’π‘¦)] = cos [Ο€/4βˆ’π‘₯+Ο€/4 βˆ’π‘¦] = cos [Ο€/4+Ο€/4βˆ’π‘₯βˆ’π‘¦] = cos [Ο€/2 βˆ’(π‘₯+𝑦) ] Putting Ο€ = 180Β° = cos [(180Β°)/2 βˆ’(π‘₯+𝑦) ] = cos [90Β° βˆ’(π‘₯+𝑦) ] = sin (π‘₯+𝑦) = R.H.S Hence proved

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