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If tan""[(pi)/4 + theta ]+tan[(pi)/(4)- ...

If `tan""[(pi)/4 + theta ]+tan[(pi)/(4)- theta ]=a " then " tan^(3)[(pi)/(4)+ theta ] + tan^(3)[(pi)/(4)- theta]=`

A

0

B

a

C

`3a`

D

`a^(3)-3a`

Text Solution

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The correct Answer is:
D
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DIPTI PUBLICATION ( AP EAMET)-TRIGONOMETRIC RATIOS AND IDENTITIES -EXERCISE 1 B ( COMPOUNDS ANGLES )
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  2. If tan(pi//4 + theta ) + tan (pi//4 - theta ) =3 , " then " tan^(2)(p...

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  3. If tan""[(pi)/4 + theta ]+tan[(pi)/(4)- theta ]=a " then " tan^(3)[(pi...

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  4. If cos alpha + cos beta =0 = sin alpha + sin beta " then " cos (alpha...

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  5. If tan theta =(cos 12^@ + sin 12^(@))/(cos 12^(@)-sin12^(@)) " then "...

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  6. If tan 20^@ =p , " then " (tan 160^@ - tan 110^(@))/(1+ tan 160^(@) ta...

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  7. If 0 lt theta lt pi//2 and 2 sin theta = sqrt(3) cos 10^(@) + sin 10^(...

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  8. If A+B=pi//2 then tan B+ 2 tan (A-B)=

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  9. If A+B=135^(@) " then " (1+ cot A ) (1+cot B)=

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

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

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

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

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

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

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

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

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

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

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

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