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If secx + tanx =4/3, then find secx.tanx. Please give a shorter method for this. Longer one I know.

If secx + tanx =4/3, then find secx.tanx. Please give a shorter method for this. Longer one I know.

Grade:12th pass

4 Answers

Vaibhav Singh
57 Points
7 years ago
Given, secx + tanx = 4/3. --------(ii)Multiply both sides by secx - tanx .Therefore, (secx + tanx)(secx - tanx) =4/3(secx - tanx).Thus secx - tanx = 3/4. -------(i)Solving (i) & (ii) we get secx = 25/24 & tanx = 7/24.Therefore secx.tanx = 175/576.
Nandana
110 Points
7 years ago
 hi ,
      Given , secx + tanx = 4/3,
           we know that 1+tan2 (x )= sec2 (x)
             =>     sec2 (x)-tan2 (x ) = 1
             =>     (sec (x) + tan (x))(sec (x) -tan(x)) = 1
                               sec (x) -tan(x) = ¾
                               sec (x) +tan(x) = 4/3
                        => sec (x) =25/24 & tan (X) = 7/24
                              sec (x) * tan (x) = 175/ 576
                                                                                     thank you !
 
 
      
Nandana
110 Points
7 years ago
 hi ,
      Given , secx + tanx = 4/3,
           we know that 1+tan2 (x )= sec2 (x)
             =>     sec2 (x)-tan2 (x ) = 1
             =>     (sec (x) + tan (x))(sec (x) -tan(x)) = 1
                               sec (x) -tan(x) = ¾
                               sec (x) +tan(x) = 4/3
                        => sec (x) =25/24 & tan (X) = 7/24
                              sec (x) * tan (x) = 0.303819444
                                                                                     thank you !
 
 
      
Adwait
21 Points
6 years ago
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