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If cos (A-B)=(1)/(2) and cot(A+B)=sqrt(3...

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

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The correct Answer is:
`A=135^(@), B=75^(@)`
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CALCUTTA BOOK HOUSE-TRIGONOMETRIC RATIOS AND TRIGONOMETRIC IDENTITIES -EXERCISE
  1. Fill in the blanks : tan theta=sqrt(3), cos theta= -(1)/(2) and 0^(...

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

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

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

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

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

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

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

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

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

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

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

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

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  14. Prove that sqrt((1+costheta)/(1-costheta))+sqrt((1-cos theta)/(1+cos ...

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  15. Prove that (sin A+sinB)/(cosB-cosA)=(cos A+cosB)/(sinA-sinB).

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  16. Prove that (sec theta-tan theta+1)/(sec theta+tan theta+1)=(1-sin the...

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  17. Prove that (1)/("cosec"alpha-cot alpha)-(1)/(sin alpha)=(1)/(sin alpha...

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  18. If "cosec" theta- sin theta=m^(3) and sec theta-cos theta=n^(3), then ...

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  19. eliminate theta : a(1) sec theta + b(1)tan theta+c(1)=0 , a(2)sec thet...

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  20. If tan theta=(a)/(b) , then find the value of (sin theta)/(cos^(8)thet...

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