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If A+B=225^(@) than prove that (cot A)/(...

If `A+B=225^(@)` than prove that `(cot A)/(1+cotA). (cot B)/(1+cotB)=(1)/(2)`

A

0

B

`1//2`

C

`1//4`

D

`3//4`

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The correct Answer is:
B
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DIPTI PUBLICATION ( AP EAMET)-TRIGONOMETRIC RATIOS AND IDENTITIES -EXERCISE 1 B ( COMPOUNDS ANGLES )
  1. If A+B=135^(@) " then " (1+ cot A ) (1+cot B)=

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  2. If A+B=45^(@), then prove that (i) (1+ tan A) (1+ tan B) =2 (ii) (cot...

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  3. If A+B=225^(@) than prove that (cot A)/(1+cotA). (cot B)/(1+cotB)=(1)/...

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  4. If alpha + beta = 3pi//4 " then " (1- tan alpha ) (1- tan beta ) =

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  5. If A, B are acute angles, sin A =4/5 , tan B=5/12 , then sin (A+B)=

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  6. If A,B are acute angle , sin 4/5 , tan B=5/12 , then cos (A-B)=

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  7. If A,B are acute angle, tan A=5/12 , cos B=3/5 , then cos (A+B)=

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  8. If A,B are acute angle , tan A=(n)/(n+1), tan B=(1)/(2n+1), " then " A...

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  9. If sin A=1//sqrt(10), sin B= 1//sqrt(5) where A and B are positive an...

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  10. If A,B,C are acute angles , tan A=1/2 , tan B=1//5 , tan C=1//8 , " th...

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  11. If B,A+B are acute angle , sin(A+B)=12/13, sin B=5/13 then sin A =

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  12. If cos A =-3//5 , sin B=7//25 and 90^(@) lt A lt 180^@,0^(@) lt B lt ...

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  13. If 270^(@) lt A lt 360^(@), 90^(@) lt B lt 180^(@) , cos A =5//13 , ta...

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  14. If 270^(@) lt A lt 360^(@), 90^(@) lt B lt 180^(@) , cos A =5//13 , ta...

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  15. If cos alpha = -12//13 , cot beta = 24//7 , 90^(@) lt alpha lt 180^(@...

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  16. If 0 lt alpha , beta lt pi//4, cos ( alpha + beta )=4//5 , sin (alpha...

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  17. If tan(picostheta)=cot(pisintheta), then prove that cos(theta-(pi)/(4...

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  18. If tan (A-B)=7//24 , tan A=4//3 " where " A,B are acute , then A+B=

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  19. If cos (A-B)=3//5 and tan A tan B=2 , then which one of the following...

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  20. If cot theta = 8//15 and theta does not lie in the first quadrant , t...

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