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x=tanA+sina y=tana-sina prove x 2- y 2= ∫4xy

x=tanA+sina     y=tana-sina prove  x2-y2=∫4xy

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1 Answers

Y RAJYALAKSHMI
45 Points
9 years ago
LHS:  
x2 – y2 = (tanA + sinA)2 – (tanA – sinA)2 = 4tanA sinA
 
RHS:
 4*sqrt(xy) = 4*sqrt(tanA + sinA)(tanA – sinA)  
= 4* sqrt(tan2A – sin2A) = 4* sqrt(sin2A/cos2A – sin2A) 
= 4* sqrt(sin2A (1 – cos2A)/ cos2A) 
= 4* sqrt(sin2A *sin2A / cos2A)
= 4* sqrt (tan2A sin2A)
= 4tanAsinA 
 
Hence, LHS = RHS

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