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If an angle alpha is divided into two ...

If an angle ` alpha ` is divided into two parts A and B such that A-B=x and tan A: tan B=k:1 , then the value of sin x is

A

`(k+1)/(k-1) sin alpha `

B

`(k)/(k+1) sin alpha `

C

`(k-1)/(k+1) sin alpha `

D

none

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Verified by Experts

The correct Answer is:
C
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DIPTI PUBLICATION ( AP EAMET)-TRIGONOMETRIC RATIOS AND IDENTITIES -EXERCISE 1 B ( COMPOUNDS ANGLES )
  1. If x= tan A - tan B , y= cot B- cot A " then " (1)/(x)+(1)/(y)=

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  2. If tan alpha , tan beta are the roots of the equation x^(2) + px+q=...

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  3. If an angle alpha is divided into two parts A and B such that A-B=x ...

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  4. In a DeltaPQR , if 3 sin P+4 cos Q=6 and 4 sin Q+3 cos P=1 , then the...

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  5. If tan beta = 2 sin alpha sin gamma " cosec "(alpha + gamma) , then ...

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  6. cos theta + cos (120^(@) + theta ) + cos (120^(@) - theta )=

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  7. cos theta + cos (240^(@) + theta ) + cos (240^(@)- theta )=

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  8. sin theta + sin (120^(@) + theta ) + sin ( theta - 120^(@))=

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  9. cos theta - cos (60^(@) + theta ) - cos(60^(@) - theta )=

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  10. cos 20^(@) + cos 100^(@) + cos 140^(@) =

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  11. sin 40^(@) - sin 80^(@)+ sin 160^(@)=

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  12. If A+B+C=0 , then tan A+ tan B+ tan C=

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  13. If A+B+C=0 , then cot A cotB + cot B cot C+ cot C cot A =

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  14. If A+C=B then tan A* tan B * tan C=

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  15. If A+B+C = pi //2 , then tanA tanB + tanB tanC+ tan A tan C=

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  16. If A=35^(@) , B= 15^(@) and C=40^(@) , then tan A* tan B+ tan B* tan...

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  17. If ABC are angle of a triangle then prove that cot Acot B+ cot Bcot C+...

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  18. If A+ B+C= pi//2 , " then " tan 2A + tan 2B+ tan 2C=

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  19. If A+B+C= pi//2 then show that cot A + cot B+ cot C=cot A cot B cot C

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  20. If A+B+C= pi//2 then show that cot A + cot B+ cot C=cot A cot B cot C

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