Ex 3.3, 18 - Chapter 3 Class 11 Trigonometric Functions

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Ex 3.3, 18 Prove that 〖sin x − 〗⁡sin⁡y /(𝑐𝑜𝑠⁡x + 𝑐𝑜𝑠⁡y ) = tan (x − y)/2 Solving L.H.S 〖sin x − 〗⁡sin⁡y /(𝑐𝑜𝑠⁡x + 𝑐𝑜𝑠⁡y ) = 〖𝟐 𝒄𝒐𝒔((𝒙 + 𝒚 )/𝟐)〗⁡〖 𝒔𝒊𝒏⁡((𝒙 − 𝒚 )/𝟐) 〗/(𝟐 𝒄𝒐𝒔⁡((𝒙 + 𝒚 )/𝟐) 𝒄𝒐𝒔⁡((𝒙 − 𝒚 )/𝟐) ) = 𝑠𝑖𝑛⁡" " ((𝑥 − 𝑦 )/2)/(𝑐𝑜𝑠⁡((𝑥 − 𝑦 )/2) ) = tan (𝒙 − 𝒚 )/𝟐 = R.H.S Hence L.H.S. = R.H.S. Hence proved

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