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pls give solution: If cos A= tan B, cos B= tan C and cos C= tan A then sin A equal to?

pls give solution: If cos A= tan B, cos B= tan C and cos C= tan A then sin A equal to?

Grade:12th pass

2 Answers

Faiz
107 Points
7 years ago
cos A= tan B ----1cos B= tan C ----2cos C= tan A ----3Multiply 2 and 3cos B cos C = tan C ( sin A / cos A )Put the value of cos A from 1 and simplify....Ans : sin A = (tan B cos B cos C) / tan C or ( sin B cos² C ) / sin C...
Vivek singh
11 Points
6 years ago
**cos C=tan A****so tan C=sqrt(1-tan ^2 A)/tan A****cos B=tan C=sqrt(1-tan ^2 A)/tan A****so tan B=sqrt((2×tan ^2 A-1)/(1-tan ^2 A))****But cos A=tan B****cos A=sqrt(2×tan ^2 A-1)/(1-tan ^2 A))****cos ^2 A=(2×tan ^2 A-1)/(1-tan ^2 A)****1/sec ^2 A=**(**2×tan ^2 A-1)/(1-tan ^2 A)****1/(1+tan ^2 A)=(2×tan ^2 A-1)/(1-tan ^2 A)****tan ^4 A +tan ^2 A -1=0****tan ^2 A=(-1+√5)/2****cot ^2 A=2/(√5 -1)****cosec ^2 A -1 =2/(√5 -1)****cosec ^2 A=(1+√5)/(√5 -1)****sin ^2 A=(√5–1)/(√5+1)=(√5–1)^2/(√5+1)(√5–1)****sin ^2 A=((√5–1)^2)/4****sin A=(√5–1)/2.**

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