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In triangle ABC, right-angled at B, if tan A = 1/√3 find the value of: (i) sin A cos C + cos A sin C (ii) cos A cos C – sin A sin C

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one month ago Anand Kumar Pandey
1583 Points
```							Dear StudentLet ΔABC in which∠B=90°tan A =BC/AB = 1/√3Let BC = 1k and AB =√3k,Where k is the positive real number of the problemBy Pythagoras theorem in ΔABC we get: AC^2=AB^2+BC^2AC^2=(√3k)^2+(k)^2AC^2=3k^2+k^2AC^2=4k^2AC = 2kNow find the values of cos A, Sin ASin A = BC/AC = 1/2Cos A= AB/AC = √3/2Then find the values of cos C and sin CSin C = AB/AC =√3/2Cos C = BC/AC = 1/2Now, substitute the values in the given problem(i) sin A cos C + cos A sin C = (1/2) ×(1/2 )+ √3/2 ×√3/2 = 1/4 + 3/4 = 1(ii) cos A cos C–sin A sin C = (√3/2 )(1/2)–(1/2) (√3/2 ) = 0Thanks
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one month ago
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