If tan a = 2/√(13), then the value of 
is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 21.
| Understanding/Application |
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tan a = 2/√(13) sec a = √(1+tan2a) cosec a = √(1+tan2a)/tan a |
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(cosec2a + 2sec2a)/(cosec2a - 3sec2a) = {(√(1+tan2a)/tan a)2 + 2√(1+tan2a)2}/{(√(1+tan2a)/tan a)2 - 3√(1+tan2a)2} = {(√(1+ ((2/√(13))2)/(2/√(13))2 + 2√(1+(2/√(13))2)2}/{(√(1+ (2/√(13))2)/(2/√(13)2)2 - 3√(1+ (2/√(13)2)2} = [{(1 + 4/13)/4/13} + 2(1 + 4/13)]/[((1 + 4/13)/4/13} - 3(1 + 4/13)] = [{17/13(13/4)} + 2(17/13)]/[{17/13(13/4)} - 3(17/13)] = (17/4 + 34/13)/(17/4 - 51/13) = (221 + 136)/(221 - 204) = 357/17 = 21 |