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If cosecA + CotA= 11/2 then tan A=? Can u pks solve this fr me

If cosecA + CotA= 11/2 then tan A=?
Can u pks solve this fr me

Grade:11

3 Answers

Vikas TU
14149 Points
7 years ago
 (cosec A + cot A) x (cosec A - cot A)/(cosec A - cot A) --->11/2 
ie (cosec^2 A - cot^2 A) /(cosec A - cot A ) --->11/2 
now cosec^2 A - cot^2 A is 1 
so 1/(cosecA - cotA) --->11/2 so cosec A - cot A --->2/11 
cosec A + cot A ---> 11/2 
subtraction gives - 2 cot A --->2/11 -11/2---> -117/22 
so cot A ---> 117/44 
now tan A ---> 1/cot A ---> 44/117
raj
383 Points
7 years ago
hello,
 (cosec A + cot A) x (cosec A - cot A)/(cosec A - cot A) --->11/2 
ie (cosec^2 A - cot^2 A) /(cosec A - cot A ) --->11/2 
now cosec^2 A - cot^2 A is 1 
so 1/(cosecA - cotA) --->11/2 so cosec A - cot A --->2/11 
cosec A + cot A ---> 11/2 
subtraction gives - 2 cot A --->2/11 -11/2---> -117/22 
so cot A ---> 117/44 
now tan A ---> 1/cot A ---> 44/117
Rishi Sharma
askIITians Faculty 646 Points
3 years ago
Dear Student,
Please find below the solution to your problem.

cosecA=1/sinA
cotA=cosA/sinA
Therefore, cosecA+cotA=(1+cosA)/sinA…..Eq 1
Now, 1+cosA=2×cos(A/2)×cos(A/2)... Eq 2… Numerator
And sinA=2sin(A/2)cos(A/2)…. Eq 3…. Denominator
Substituting Eq 2 and Eq 3 in Eq 1, we get:
Numerator/denominator= 11/2 as RHS is given in question
cot (A/2)=11/2
Or tan(A/2)=2/11
We know that
tanA=[(2 tan(A/2)]/[1-sqr(tan(A/2)
Where sqr is a squaring function(ex: sqr(2)=4)
Substituting value of tan(A/2) in the above eq, we get
tanA=44/117.

Thanks and Regards

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