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Prove each of the following identities :...

Prove each of the following identities :
`(i) 1+ (cot^(2) theta)/((1+ "cosec"theta))= "cosec" theta `
` (ii) 1+ (tan^(2) theta)/((1+ sec theta))= sec theta `

Text Solution

Verified by Experts

(i) Write `cot^(2)theta=("cosec"^(2)theta -1).`
(ii) Write `tan^(2)theta=(sec^(2)theta-1).`
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Prove each of the following identities : (i) (sec^(2) theta -1) cot^(2) theta =1 " " (ii) (sec^(2) theta -1) ("cosec"^(2)theta -1) =1 (iii) (1- cos^(2) theta )sec^(2) theta = tan^(2) theta

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RS AGGARWAL-TRIGONOMETRIC IDENTITIES-Exercise 13A
  1. Prove each of the following identities : (1)/((1+ sin theta)) + (1)/...

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  2. Prove each of the following identities : (i) sec theta(1- sin theta)...

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  3. Prove each of the following identities : (i) 1+ (cot^(2) theta)/((1+...

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  4. Prove each of the following identities : ((1+ tan^(2) theta) cot th...

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  5. Prove each of the following identities : (tan^(2) theta)/((1+ tan^(...

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

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  7. Prove each of the following identities : (tan theta)/((1-cot theta)...

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  8. Prove each of the following identities : ( cos^(2) theta)/((1- tan t...

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  9. Prove each of the following identities : (cos theta) /((1- tan thet...

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  10. Prove each of the following identities : (1+ tan^(2) theta)(1+ cot^(...

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  11. Prove each of the following identities : (tan theta)/((1+ tan^(2) t...

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  12. Prove each of the following identities : (i) sin^(6) theta + cos^(6...

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  13. Prove each of the following identities : (i) (1- tan^(2) theta)/(1+ ...

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  14. Prove each of the following identities : (i) (tan theta)/((sec theta...

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  15. Prove each of the following identities : (i) (sec theta -1)/(sec the...

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  16. Prove each of the following identities : (i) sqrt((1+ sin theta)/(1-...

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  17. Prove each of the following identities : (cos^(3) theta + sin^(3) th...

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  18. Prove each of the following identities : (sin theta)/((cot theta + "...

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  19. Prove each of the following identities : (i) (sin theta - cos theta)...

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  20. Prove each of the following identities : (1+ cos theta - sin^(2) th...

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