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Prove each of the following identities :...

Prove each of the following identities :
` (sin theta)/((1+ cos theta)) + ((1+ cos theta))/(sin theta) = 2 "cosec" theta `

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(sin theta)/((1+cos theta))+((1+cos theta))/(sin theta)=2cosec theta

Prove each of the following identities : (sin theta)/((cot theta + "cosec" theta )) - (sin theta)/((cot theta - "cosec" theta))= 2

Prove each of the following identities : (sin theta + cos theta)/(sin theta - cos theta) + (sin theta - cos theta)/(sin theta + cos theta) = (2) /((sin^(2) theta - cos^(2) theta)) = (2) /((2sin^(2) theta -1))

Prove each of the following identities : ( cos^(2) theta)/((1- tan theta)) + (sin^(3) theta)/((sin theta - cos theta)) = (1+ sin theta cos theta)

Prove each of the following identities : (i) (sin theta - cos theta)/(sin theta + cos theta) + ( sin theta+ cos theta)/(sin theta - cos theta) = (2)/((2 sin^(2) theta -1)) (ii) (sin theta + cos theta ) /(sin theta - cos theta) + ( sin theta - cos theta) /(sin theta + cos theta) = (2) /((1- 2 cos^(2) theta))

Prove each of the following identities : (cos theta) /((1- tan theta)) - (sin^(2) theta)/((cos theta - sin theta)) = (cos theta + sin theta)

Prove the following identities: (cos theta)/(1-sin theta)+(cos theta)/(1+sin theta)=2sec theta

Prove each of the following identities : (i) (1+ cos theta + sin theta)/(1+ cos theta - sin theta) =(1+ sin theta)/(cos theta) (ii) (sin theta + 1- cos theta)/(cos theta - 1 + sin theta) = (1+ sin theta)/(cos theta)

Prove each of the following identities : (i) (1+ cos theta)(1- cos theta)(1+ cot^(2) theta)=1 (ii) "cosec" theta (1+ cos theta)("cosec" theta - cot theta)=1

EDUCART PUBLICATION-INTRODUCTION TO TRIGNOMETRY AND ITS APPLICATIONS -SHORT ANSWER (SA-II) TYPE QUESTIONS
  1. Prove that (sin theta - cos theta +1)/(sin theta + cos theta -1) = (...

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  2. Prove that sqrt[(1+sinA)/(1 - sinA)] = secA + tanA

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  3. Prove each of the following identities : (sin theta)/((1+ cos theta...

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  4. If sin theta+cos theta=sqrt(2) then prove that tan theta+cot theta=2

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  5. Prove that (cot theta + "cosec" theta -1 )/(cot theta - "cosec" thet...

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  6. Prove : 2(sin^(6)theta+cos^(6)theta)-3(sin^(4)theta+cos^(4)theta)+1=0.

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  7. If sin theta+cos theta=sqrt3, then prove that tan theta+cot theta=1

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  8. Prove that : (sin^(4)theta- cos^(4) theta+ 1) "cosec"^(2)theta=2

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  9. Prove that : (2 cos^(2) theta-cos theta)/(sin theta-2 sin^(3)theta)=...

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  10. If tanA=(3)/(4), then show that sin A cos A=(12)/(25)

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  11. Prove that: (tantheta/(1-tantheta))-(cottheta/(1-cottheta))=(costheta+...

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  12. If costheta+sintheta=sqrt(2)costheta, show that costheta-sintheta=sqrt...

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  13. Prove that: (tanA + tanB)/(cotA+cotB)=tanAtanB

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  14. A ladder 15 metres long just reaches the top of a vertical wall. If th...

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  15. Prove that: sqrt((sectheta -1)/(sec theta +1)) + sqrt((sec theta +1)/(...

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  16. Prove that (sin theta + "cosec" theta)^(2)+(cos theta + sec theta)^(...

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  17. Prove that: (1 + cot A - "cosec"A)(1 + tanA + secA) =2

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  18. If 4 tan theta = 3, evaluate (4 sin theta - cos theta +1)/(4 sin theta...

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  19. A player sitting on the top of a tower of height 20 m observes the ang...

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  20. Using the formula cos 2theta = 2 cos^(2)theta - 1, find the value of c...

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