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if secA+tanA=x,then what are the values of sinA,secA,tanA

if secA+tanA=x,then what are the values of sinA,secA,tanA

Grade:10

4 Answers

siddharth gupta
28 Points
9 years ago
secA+tanA=x.........(1.) and we know that sec2A-tan2A=1 ON DIVIDING with  given result with eqn.1secX-tanX=1/x(2.)
now solve eqn(1.)and(2.) by simple linear  equation method to obtain required ratios. 
mihir
21 Points
7 years ago
(secA+tanA)(secA-tanA)=1
secA-tanA=1/x  -i)
secA+tanA=x  -ii)
Adding i) and ii)
2secA=(x2​ +1)/x
secA=(X2 ​+1)/2x
​tanA=(x2 ​-1)/2x​
sinA=tanA/secA=(x2​ -1)/(x 2 ​+1)​ ​​
 
 
MD danish
15 Points
4 years ago
We have,
      SecA+tan=x........(1)
Now,according to formula we have,Sec2A-tan2A=1by using it we can write
 Sec2A-tan2A=(secA+tanA)(SecA-tanA).........(2)
By putting the value of secA+TanA in eq1 then we have (x)(secA-tanA)=1
SecA-tanA=1/x,.... ....eq(3)
By subtracting eq. 1 & eq. 3 then,
(SecA+TanA)-(secA-tanA)=x-(1/x)
SecA+tanA-secA+TanA=x2-1/x
2tanA=x2-1/x
TanA=x2-1/2x answer...
           
Rishi Sharma
askIITians Faculty 646 Points
3 years ago
Dear Student,
Please find below the solution to your problem.
sec^2 A – tan^2 A = 1
(secA+tanA)(secA-tanA) = 1
secA-tanA = 1/x -i)
secA+tanA = x -ii)
Adding i) and ii)
2secA = (x^2​ +1)/x
secA = (X^2 ​+1)/2x
​tanA = (x^2 ​-1)/2x​
sinA = tanA/secA
= (x^2​-1)/(x^2 ​+1)

Thanks and Regards

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