Given that:
sec x+tan x=22/7.
Determine the value of:
csc x + cot x
This might be solvable by identities alone, but this algebraic method worked ok.
1/cosx + sinx/cosx = 22/7
(1+sinx)/cos(x)=22/7
(1+sinx)/sqrt(1-sin^2x)=22/7
7(1+sinx)=22sqrt(1-sin^2x)
49(1+sinx)^2=484(1-sin^2x)
533sin^2x+98sinx-435=0
this is a quadratic in sinx, solving gives
sinx = 435/533
from which cosx=308/533
The expression to find can be written as (1+cosx)/sinx
Substituting the values gives the solution 29/15
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Posted by Jer
on 2023-10-27 08:44:32 |
Possible solution
