Math, asked by junaidAnisar, 1 year ago

secA + tanA = x Find the value of tanA

Answers

Answered by gangstar2000
3
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Answered by guptaramanand68
1

 \sec(A) +  \tan(A)  = x \:  \:  \: (1)  \\  \\  { \sec }^{2} (A) -  \tan ^{2} (A ) = 1 \\ ( \sec(A)  +  \tan(A) )( \sec(A)  -  \tan(A) ) = 1 \\ x( \sec(A)  -  \tan(A) ) = 1 \\  \sec(A)  -  \tan(A)  =  \frac{1}{x}  \\  \text{Subtract this result  from the (1) } \\ 2 \tan(A)  = x -   \frac{1}{x}  \\ 2 \tan(A)  =  \frac{ {x}^{2} - 1 }{x}  \\  \boxed{ \tan(A)  =  \frac{ {x}^{2}  - 1}{2x}}
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