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Example 13 - Prove sin (x+y) / sin (x-y) = tan x + tan y - Examples

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Example 13 - Chapter 3 Class 11 Trigonometric Functions - NCERT Prove that sin⁡〖(𝑥+𝑦) 〗/sin⁡〖(𝑥−𝑦) 〗 = tan⁡〖𝑥 + tan⁡𝑦 〗/tan⁡〖𝑥 −tan⁡𝑦 〗 L.H.S. sin⁡〖( 𝑥 + 𝑦)〗/sin⁡〖( 𝑥 − 𝑦)〗 = (sin⁡𝑥 cos⁡𝑦 + 〖𝑐𝑜𝑠 𝑥 sin〗⁡𝑦)/(sin⁡𝑥 cos⁡𝑦 − 〖𝑐𝑜𝑠 𝑥 sin〗⁡𝑦 ) R.H.S. tan⁡〖𝑥 + tan⁡𝑦 〗/(tan⁡𝑥 − tan⁡𝑦 ) = (sin⁡𝑥/cos⁡𝑥 + sin⁡𝑦/cos⁡𝑦 )/(sin⁡𝑥/cos⁡𝑥 − sin⁡𝑦/cos⁡𝑦 ) = ((sin⁡𝑥 cos⁡𝑦 + 〖𝑐𝑜𝑠 𝑥 sin〗⁡𝑦)/cos⁡〖𝑥 cos⁡𝑦 〗 )/((sin⁡𝑥 cos⁡𝑦 − 〖𝑐𝑜𝑠 𝑥 sin〗⁡𝑦)/cos⁡〖𝑥 cos⁡𝑦 〗 ) = (sin⁡𝑥 cos⁡𝑦 + 〖𝑐𝑜𝑠 𝑥 sin〗⁡𝑦)/(sin⁡𝑥 cos⁡𝑦 − 〖𝑐𝑜𝑠 𝑥 sin〗⁡𝑦 ) = L.H.S Hence L.H.S = 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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.