Question

sec a+tan a=4/3 then sec a* tan a=?

Answer 1

Given:

• secA + tanA = 4/3.

To Find:

• Value of secA × tanA.

Answer:

We are here given that , secA + tanA = 4/3.

Let secA + tanA = 4/3 .............(1)

Now we know relationship b/w tan and sec as ,

$\large{\boxed{\red{\bf{\leadsto sec^2\theta - tan^2\theta = 1}}}}$

=> sec²∅ - tan²∅ = 1.

=> (sec∅ + tan∅ )(sec∅-tan∅) = 1.

=> (sec∅-tan∅) = 1/ sec∅+tan∅.

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Now ,

=> secA + tanA = 4/3.

=> secA - tanA = 1÷4/3.

=> secA - tanA = 3/4. ............(2)

(1)+(2)

=> secA + tanA + secA - tanA = 3/4+4/3.

=> 2secA = 9+16/12.

=> 2secA = 25/12.

=> secA = 25/24.

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Putting this is (1) ,

=> secA + tanA = 4/3.

=> 25/24 + tanA = 4/3.

=> tanA = 4/3-25/24.

=> tanA = 32-25/24.

=> tanA = 7/24.

Hence tanA × secA

= 25/24 × 7/24

= 175/576.