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Sec theta +Tan theta =x then what is the value of tan theta

Sec theta +Tan theta =x then what is the value of tan theta

Grade:10

3 Answers

Arun
25750 Points
6 years ago
Dear Khushi
 
I have taken P in place of theta because of simplicity in writing
 
sec p = x – tan p
 
squaring both the sides
 
sec2 p  = x2 – 2* x* tan p + tan2 p
sec2 p – tan2 p = x2 – 2* x* tan p
x2 – 2* x* tan p – 1 = 0
2* x* tan p = x2 – 1
tan p = (x2 – 1) / 2 x
 
Regards
Arun (askIITians forum expert)
 
Sripad Sambrani
22 Points
4 years ago
Taken A for theta
 
Given SecA+tanA=x then secA-tanA=1/x
subtracting latter from the first, we have
=> 2tanA=x-(1/x)=(x^2-1)/x
=> tanA=(x^2-1)/2x
SM
13 Points
4 years ago
Sec theta + tab theta = X ( given )............eq1
Sec²theta - tan ²theta = 1
( Sec theta + tan theta )( sec theta - tan theta) = 1
X × ( sec theta - tan theta ) = 1
Sec theta - tan theta = 1/X ..........eq 2 
 
Sec theta + tan theta = X
Sec theta - tan theta = 1/X
_____________________________
2sec theta = X + 1/X
Sec theta = x²+1/ 2x
 
Sec theta + tan theta =X
X²+1/2x + tan theta = X
Tan theta = X - (x²+1/2x)
_________________________
Tan theta = 2x²- x²-1/2x    ........is the required answer
_________________________ 
 
Tan theta = x²-1/2x
Sec theta + tan theta = X 
Sec theta - tan tgeta

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