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Evaluate each of the following: cot 12^@...

Evaluate each of the following: `cot 12^@cot 38^@cot52^@cot60^@cot78^@`
`tan5^@tan25^@tan30^@tan65^@tan85^@`

A

`sqrt(3)`

B

`(1)/(sqrt(3))`

C

1

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Given expression `=(tan5^(@)tan85^(@))(tan25^(@)tan65^(@))tan30^(@)`
`={tan5^(@)*tan(90^(@)-5^(@))}{tan25^(@)*tan(90^(@)-25^(@))}*tan30^(@)`
`=(tan5^(@)*cot5^(@))(tan25^(@)*cot25^(@))*(1)/(sqrt(3))=1xx1xx(1)/(sqrt(3))=(1)/(sqrt(3)).`
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RS AGGARWAL-TRIGONOMETRIC IDENTITIES-Multiple Choice Questions (Mcq)
  1. (tan 35^(@))/(cot 55^(@))+(cot 78^(@))/(tan 12^(@))=?

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  2. Choose the correct answer in each of the following questions: tan 1...

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  3. Evaluate each of the following: cot 12^@cot 38^@cot52^@cot60^@cot78^@ ...

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  4. cos1^@xxcos2^@xxcos3^@xx...xxcos180^@=?

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  5. Evaluate : (2sin^2 63^@+1+2sin^2 27^@)/(3 cos ^2 17^@-2+3cos^2 73^@)

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  6. Choose the correct answer in each of the following questions: sin47^...

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  7. sec70^(@)sin20^(@)+cos20^(@)"cosec"70^(@)=?

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  8. If sin 3A =cos(A-10^(@)) where 3A is an acute angle , then find the va...

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  9. If sec 4A="cosec"(A-10^(@))and 4A" is acute then " angle A=?

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  10. Choose the correct answer in each of the following questions: If A a...

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  11. Choose the correct answer in each of the following questions: If c...

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  12. Choose the correct answer in each of the following questions: sin(45...

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  13. Choose the correct answer in each of the following questions: sec^(2...

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  14. Choose the correct answer in each of the following questions: "cosec...

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  15. Choose the correct answer in each of the following questions: (2tan^...

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  16. Find the value of [(sin^2 2 2^(@)+sin^2 6 8^(@))/(cos^2 2 2^(@)+cos^2 ...

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  17. Without using trigonometric tables , evaluate the following : (co...

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  18. Choose the correct answer in each of the following questions: (cos38...

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  19. If 2sin 2 theta =sqrt(3) " then " theta=?

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  20. Choose the correct answer in each of the following questions: If 2co...

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