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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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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) Solving 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 Where 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 [(𝝅/πŸ’βˆ’π’™)" " +(𝝅/πŸ’ βˆ’π’š)] = cos [Ο€/4βˆ’π‘₯+Ο€/4 βˆ’π‘¦] = cos [Ο€/4+Ο€/4βˆ’π‘₯βˆ’π‘¦] = cos [Ο€/4+Ο€/4βˆ’π‘₯βˆ’π‘¦] = cos [𝝅/𝟐 " " βˆ’(𝒙+π’š)] Putting Ο€ = 180Β° = cos [(180Β°)/2βˆ’(π‘₯+𝑦)] = cos [90Β° βˆ’(π‘₯+𝑦)] = sin (𝒙+π’š) = R.H.S Hence proved = cos [(𝝅/πŸ’βˆ’π’™)" " +(𝝅/πŸ’ βˆ’π’š)] = cos [Ο€/4βˆ’π‘₯+Ο€/4 βˆ’π‘¦] = cos [Ο€/4+Ο€/4βˆ’π‘₯βˆ’π‘¦] = cos [Ο€/4+Ο€/4βˆ’π‘₯βˆ’π‘¦] = cos [𝝅/𝟐 " " βˆ’(𝒙+π’š)] Putting Ο€ = 180Β° = cos [(180Β°)/2βˆ’(π‘₯+𝑦)] = cos [90Β° βˆ’(π‘₯+𝑦)] = sin (𝒙+π’š) = R.H.S Hence proved

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.