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In a `Delta ABC `, if A,B,C are in AP, then `(a)/(c) sin2C+(c)/(a)(sin2A)` is equal toA. `(1)/(2)`B. `(sqrt(3))/(2)`C. 1D. `sqrt(3)` |
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Answer» Correct Answer - D Since ,`A,B and C ` are in AP `therefore A+C=2B` `rArr (A+C)+B=2B+B` `rArr 180^@=3BrArr =60^@`....(ii) `(a)/(c)(sin2C)+(c)/(a)(sin2A)` `=(2a)/(c)(sinC cos C)+(2c)/(a)(sinA cos A)` `=2a((sinC)/(c))cos C+2c((sinA)/(a))cosA` `=2(ak)cos C +2(ck)cos A` `=2(sin A cos C+sinB` `[sin(a+phi)=sinthetacosphi+sinphicostheta]` `=2 sin 60^@=2(sqrt(3)//2)=sqrt(3)`. |
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