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Prove that sqrt((1+cos30^(@))/(1-cos30^...

Prove that `sqrt((1+cos30^(@))/(1-cos30^(@)))=sec 60^(@)+tan60^(@)`.

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`LHS=sqrt((1+cos30^(@))/(1-cos30^(@)))=sqrt((1+(sqrt(3))/(2))/(1-(sqrt(3))/(2)))=sqrt(((2+sqrt(3))/(2))/((2-sqrt(3))/(2)))=sqrt((2+sqrt(3))/(2-sqrt(3)))`
`=sqrt(((2+sqrt(3))(2+sqrt(3)))/((2-sqrt(3))(2+sqrt(3))))=sqrt(((2+sqrt(3))^(2))/(4-3))=sqrt((2+sqrt(3))^(2))=2+sqrt(3)`
`RHS=sec60^(@)+tan60^(@)`
`=2+sqrt(3)`
`therefore LHS=RHS`. [Proved]
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CALCUTTA BOOK HOUSE-TRIGONOMETRIC RATIOS AND TRIGONOMETRIC IDENTITIES -EXERCISE
  1. Prove that sqrt((1+cos30^(@))/(1-cos30^(@)))=sec 60^(@)+tan60^(@).

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  2. If tan theta=(p)/(q), what is the value of (p sec theta-q " cosec" t...

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  3. In DeltaABC, right angled at B, AB:AC=1:sqrt(2), then (2 tan A)/(1-ta...

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  4. (sin30^(@)cos45^(@))/(tan 60^(@)) is equal to

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  5. In DeltaABC, If angleC=90^(@), angleA=60^(@) and AB=40 cm, then AC is ...

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  6. Write true of false : cot theta=(cos theta)/(sin theta)

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  7. Write true of false : sin theta is a product of sin and theta.

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  8. Fill in the blanks : The trigonometric ratio cos theta= ul(" ...

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  9. Fill in the blanks : The value of sin theta can never be greate th...

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  10. Fill in the blanks : The value of cot 0^(@) is not .

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  11. Find the value of cos(-1170^(@)).

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  12. Calculate the value of sec(-1680^(@)) sin 330^(@).

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  13. Simplify : sin 300^(@) cos 390^(@) tan (-855^(@))+cos(-120^(@))* sin ...

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  14. Prove that tan 225^(@) cot 405^(@)+tan 765^(@) cot 675^(@)=0.

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

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

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

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

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

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

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

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