Prove that (sina/coseca-1)+(cosa/1+seca)=Sina. cosa/(sina-cosa)
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LHS ≠ RHS for (sina/coseca-1)+(cosa/1+seca)=Sina. cosa/(sina-cosa)
so given data is wrong
Step-by-step explanation:
Sina/(coseca - 1) + Cosa/(1 + seca) = Sina.Cosa/(Sina - Cosa)
Lets tale a = 30°
LHS
= Sin30/(cosec30 - 1) + Cos30/(1 + sec30)
= (1/2)/(2 - 1) + (√3 / 2)/(1 + 2/√3)
= 1/2 + (3/2)/(√3 + 2)
= 1/2 + (3/2)(2 - √3)
= ( 1 + 6 - 3√3)/2
= ( 7- 3√3)/2
RHS
Sin30.Cos30/(Sin30 - Cos30)
= ((1/2)(√3 / 2)/(1/2 - √3 / 2)
= (√3 / 2)/(1 - √3)
= - (√3 / 4)(1 + √3)
= -(3 + √3)/4
LHS ≠ RHS
so given data is wrong
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