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What will be the value of following iden...

What will be the value of following identities :
`(cot^(2) theta (sec theta -1))/((1+ sin theta))+ (sec^(2)theta (sintheta -1))/((1+ sec theta)) `

A

`0`

B

`1`

C

`2`

D

`3`

Text Solution

Verified by Experts

The correct Answer is:
A
`LHS =(cot^(2)theta(sec^(2)theta-1)+sec^(2)theta (sin^(2)theta-1))/((1+sintheta)(1+sec theta))=((cot^(2)thetatan^(2)theta)-(sec^(2)thetacos^(2)theta))/((1+sintheta)(1+sec theta))=0.`
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RS AGGARWAL-TRIGONOMETRIC IDENTITIES-Exercise 13A
  1. Prove each of the following identities : (i) (tan theta)/((sec theta...

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

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

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

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

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

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

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  8. Prove each of the following identities : (i) ("cosec"theta + cot the...

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  9. Prove each of the following identities : (i) (1+ cos theta + sin the...

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  10. Prove that (sin theta)/(sec theta+tan theta-1)+cos theta/(cosec theta+...

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  11. Prove each of the following identities : (sin theta + cos theta)/(s...

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  12. (cos theta cosec theta-sin theta sec theta)/(cos theta+sin theta)=cose...

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  13. Prove each of the following identities : (1+ tan theta + cot theta )...

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  14. What will be the value of following identities : (cot^(2) theta (sec...

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  15. Prove the following identity: (1/(sec^2theta-cos^2theta)+1/(cos e c^2t...

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  16. Prove each of the following identities : ((sin A - sin B))/((cos A ...

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

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  18. Show that none of the following is an identity: (i) cos^(2) theta +...

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  19. Prove that: (sin theta - 2 sin^(3) theta) = (2cos^(3) theta - cos the...

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  20. If 1+sin^2 theta= 3 sintheta cos theta, then prove that tan theta = 1 ...

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