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Prove that "tan"(pi)/(12) "tan"(pi)/(16...

Prove that ` "tan"(pi)/(12) "tan"(pi)/(16) "tan"(5pi)/(12)"tan"(7pi)/(16)=1`

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CALCUTTA BOOK HOUSE-TRIGONOMETRIC RATIOS AND TRIGONOMETRIC IDENTITIES -EXERCISE
  1. Prove that tan 225^(@) cot 405^(@)+tan 765^(@) cot 675^(@)=0.

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  2. Evalute : "sin"^(2)(pi)/(4) + "cos"^(2) (3pi)/(4)+"cos"^(2)(5pi)/(4)...

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  3. Prove that "tan"(pi)/(12) "tan"(pi)/(16) "tan"(5pi)/(12)"tan"(7pi)/(1...

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  4. If tan 35^(@)=x, then prove that (tan 145^(@)- tan 125^(@))/(1+tan14...

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  5. Find the value of sin^(3)60^(@) cot 30^(@)-2 sec^(2) 45^(@)+3 cos60^(@...

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  6. If (cos theta)/(1-sin theta)-(costheta)/(1+sin theta)=2, then find the...

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  7. If (cos x)/(cosy)=n and (sinx)/(siny)=m, what is the value of (m^(2)...

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  8. If x cos 60^(@)+y cos0^(@)=3 and 4x sin 30^(@) -y cot 45^(@)=2, then ...

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  9. In DeltaPQR, angleQ=90^(@). If angleP=alpha, angleR=beta, PQ=3 and QR...

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

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

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

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

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

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

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

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

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

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

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

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