Question

if secA+tanA=4/3 then secA.tanA ​

Answer 1

Answer:

secAtanA = 175/576

Explanation:

secA+tanA = 4/3---(1)

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We know the Trigonometric identity:

sec²A-tan²A = 1

Or

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

Or

secA-tanA = 1/(secA+tanA)

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Now,

secA-tanA = 1/(secA+tanA)

=1/(4/3)

= 3/4 ----(2)

Add (1)&(2) , we get

2secA = 4/3+3/4

=> 2secA = (16+9)/12

=> secA = 25/24 --(3)

And

Subtract (2) from (1), we get

2tanA = 4/3-3/4

=> 2tanA = (16-9)/12

=> tanA = 7/24 ---(4)

Now ,

secAtanA = (25/24)(7/24)

= 175/576

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