Question

secA-tanA=1/2, then the value of secA is​

Answer 1

Answer:

Sec A = 1/2 + tan A

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It is the General format......

Answer 2

secA-  tanA = 1/2, then the value of sec A is​ $\frac{5}{4}$

Solution:

Given that sec A - tan A = 1/2

We have to find value of sec A

We know from trigonometric identities,

$\sec ^{2} A-\tan ^{2} A=1$

$\text { Using } a^{2}-b^{2}=(a+b)(a-b) \text { we get }$

$(\sec A+\tan A)(\sec A-\tan A)=1$

Substitute $sec A - tan A = \frac{1}{2}$

$(\sec A+\tan A) \times \frac{1}{2}=1$

$\sec A+\tan A=2$  ---- eqn 1

Let the given equation, $\sec A-\tan A=\frac{1}{2}$  --- eqn 2

Now add eqn 1 and eqn 2,

$(\sec A+\tan A)+(\sec A-\tan A)=2+\frac{1}{2}$

$Sec A + tanA + secA - tanA = \frac{5}{2}\\\\2secA = \frac{5}{2}\\\\secA = \frac{5}{4}$

Hence the value of Sec A is $\frac{5}{4}$

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