Question

if secA+tanA=x ....then tanA=?? please solve it step by step​

Answer 1

Answer :

tanA = (x² - 1)/2x

Solution :

• Given : secA + tanA = x
• To find : tanA = ?

We have ,

secA + tanA = x --------(1)

Also ,

We know that , sec²A - tan²A = 1

Now ,

=> sec²A - tan²A = 1

=> (secA - tanA)·(secA + tanA) = 1

=> (secA - tanA)·x = 1

=> secA - tanA = 1/x --------(2)

Now ,

Subtracting eq-(2) from (1) , we get ;

=> (secA + tanA) - (secA - tanA) = x - 1/x

=> secA + tanA - secA + tanA = x - 1/x

=> 2tanA = (x² - 1)/x

=> tanA = (x² - 1)/2x

Hence ,

tanA = (x² - 1)/2x