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What is the value of cot 15 o + cot 75 o + cot 135 o - cosec 30 o ?

What is the value of cot 15o + cot 75o + cot 135o - cosec 30o?


 


 

Grade:Upto college level

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:1
A = cot15 + cot 75 + cot135 - cosec30
cot75 = cot(90-15) = tan15
A = cot15 + tan15 + cot135 - cosec 30
tan15 = tan(45-30) = \frac{tan45 - tan30}{1+ tan45.tan30} = \frac{1-(3)^{-1/2}}{1+(3)^{1/2}}
tan15 = \frac{3^{1/2}-1}{3^{1/2}+1}
A = (\frac{3^{1/2}+1}{3^{1/2}-1}) + (\frac{3^{1/2}-1}{3^{1/2}+1}) + (-1) - (2)
A = 1
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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