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If (1+tanA)(1+tanB)=2, then tan(A+B)=...

If `(1+tanA)(1+tanB)=2`, then `tan(A+B)=`

A

-1

B

0

C

`(1)/(2)`

D

1

Text Solution

Verified by Experts

The correct Answer is:
D
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CALCUTTA BOOK HOUSE-TRIGONOMETRIC RATIOS AND TRIGONOMETRIC IDENTITIES -EXERCISE
  1. If cos theta ge (1)/(2) in the first quardrant, which one of the follo...

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  2. If A=sin^(4) theta+cos^(4) theta, then which one of the followings is...

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  3. If (1+tanA)(1+tanB)=2, then tan(A+B)=

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  4. Write 'true' or 'false' : sec theta=(2xy)/(x^(2)+y^(2))

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  5. Write 'true' or 'false' : sin theta=(x^(2)+y^(2))/(2xy)

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  6. Fill in the blanks : If sin^(4)A+sin^(2)A=1, then cot^(4)A+cot^(2)...

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  7. Fill in the blanks : "tan"(pi)/(16) "tan"(3pi)/(16)"tan"(5pi)/(16)"t...

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  8. Fill in the blanks : tan theta=sqrt(3), cos theta= -(1)/(2) and 0^(...

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  9. If theta lies in the fourth quadrant and sec theta=(5)/(3), then the ...

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  10. If cos (A-B)=(1)/(2) and cot(A+B)=sqrt(3), then find the least positiv...

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  11. If n be an integer, then find the value of tan{(npi)/(2)+(-1)^(n).(pi...

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  12. Find the least value of (2 sin^(2)theta+3 cos^(2)theta).

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  13. If cos theta+sectheta=sqrt(3), then prove that cos^(3)theta+sec^(3)the...

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  14. If 3 sin theta+4 cos theta=5, then prove that sin theta=(3)/(5).

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  15. If sin theta+"cosec"theta=2, then prove that sin^(7) theta+"cosec"^(7)...

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  16. If cos theta-sin theta=sqrt(2)cos theta, then prove that cos theta+sin...

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  17. If (a^(2)-b^(2))sin theta+2 ab cos theta-(a^(2)+b^(2))=0, then prove t...

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  18. Prove that tan theta+sqrt((1-sintheta)/(1+sin theta))=sec theta.

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  19. Prove that (tan theta+sec theta)^(2)=(1+sin theta)/(1-sin theta).

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  20. Prove that (tan theta)/(sec theta-1)+(tan theta)/(sec theta+1)=2 "cose...

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