If 40 cot A = 9, then the value of Sin A + Cos A/ Sin A - Cos A is ?
Answers
Step-by-step explanation:
Given:-
40 Cot A = 9
To find:-
Find the value of
(Sin A + Cos A)/ (Sin A - Cos A)?
Solution:-
Given that
40 Cot A = 9
=> Cot A = 9
On squaring both sides then
=> Cot^2 A = 81
=> 1 + Cot^2 A = 1+81
=> 1+Cot^2 A = 82
We know that
Cosec^2 A - Cot^2 A = 1
Cosec^2 A= 1+ Cot^2 A
=> Cosec^2 A = 82
=> Cosec A = √82
=> 1/ Sin A = √82
=> Sin A = 1/√82--------------(1)
=> Sin^2 A = (1/√82)^2
=> Sin^2 A = 1/82
=> 1 - Sin^2 A = 1-(1/82)
=> 1-Sin^2 A = (82-1)/82
=> 1-Sin^2 A = 81/82
We know that
Sin^2 A + Cos^2 A = 1
=> Cos^2 A = 81/82
=> Cos A =√(81/82)
=> Cos A = 9/√82------------(2)
Now
Sin A + Cos A = (1/√82)+(9/√82)
=> Sin A+ Cos A = (1+9)/√82
Sin A + Cos A = 10/√82
and
Sin A - Cos A = (1/√82)- (9/√82)
=> Sin A - Cos A = (1-9)/√82
Sin A - Cos A = -8/√82
Now ,
(Sin A + Cos A)/ (Sin A - Cos A)
=> (10/√82)/(-8/√82)
=> 10/-8
=> -10/8
=> -5/4
(Sin A + Cos A)/ (Sin A - Cos A) = -5/4
Answer:-
The value of
(Sin A + Cos A)/ (Sin A - Cos A) for the given problem is -5/4
Used formulae:-
- Cosec^2 A - Cot^2 A = 1
- Sin^2 A + Cos^2 A = 1
- Cosec A = 1/ Sin A
Answer:
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