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If sec(alpha-beta)=sqrt(2) and sin(alph...

If `sec(alpha-beta)=sqrt(2) and sin(alpha+beta)=(1)/(2)`, then find the least positive values of `alpha and beta`.

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The correct Answer is:
`alpha=97.5^(@), beta=52.5^(@)`
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CALCUTTA BOOK HOUSE-TRIGONOMETRIC RATIOS AND TRIGONOMETRIC IDENTITIES -EXERCISE
  1. In DeltaPQR, angleQ=90^(@). If angleP=alpha, angleR=beta, PQ=3 and QR...

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  2. If tan^(2) 45^(@)-cos^(2) 60^(@)=x sin 45^(@) cos45^(@) tan 60^(@), t...

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  3. If sec(alpha-beta)=sqrt(2) and sin(alpha+beta)=(1)/(2), then find the...

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  4. If sin27^(@)=0.454, then find the value of cos 243^(@) .

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  5. If tanA+sinA=p and tanA-sinA=q, then which one of the following is cor...

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  6. If cos theta ge (1)/(2) in the first quardrant, which one of the follo...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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