Last updated at Feb. 12, 2020 by Teachoo
Transcript
Ex 3.3, 18 Prove that 〖sin x − 〗siny /(𝑐𝑜𝑠x + 𝑐𝑜𝑠y ) = tan (x − y)/2 Solving L.H.S 〖sin x − 〗siny /(𝑐𝑜𝑠x + 𝑐𝑜𝑠y ) = 〖2 𝑐𝑜𝑠((𝑥 + 𝑦 )/2)〗〖 𝑠𝑖𝑛((𝑥 − 𝑦 )/2) 〗/(2 𝑐𝑜𝑠((𝑥 + 𝑦 )/2) 𝑐𝑜𝑠((𝑥 − 𝑦 )/2) ) We Know that sin x – sin y = 2 cos ((𝑥 + 𝑦 )/2) sin ((𝑥 − 𝑦 )/2) & cos x + cos y = 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
Ex 3.3
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