$\frac{2}{5}$
The problem asks us to find the value of $secA - tanA$ given the equation $secA + tanA = \frac{5}{2}$. We can solve this using a fundamental trigonometric identity.
Using Trigonometric Identity
We know the Pythagorean identity involving secant and tangent:
$sec^2A - tan^2A = 1$
This identity can be factored as a difference of squares:
$ (secA - tanA)(secA + tanA) = 1 $
Solving for secA - tanA
We are given that $secA + tanA = \frac{5}{2}$. Substitute this value into the factored identity:
$ (secA - tanA) \left( \frac{5}{2} \right) = 1 $
To find $secA - tanA$, we rearrange the equation:
$ secA - tanA = \frac{1}{\frac{5}{2}} $
$ secA - tanA = \frac{2}{5} $
Therefore, the value of $secA - tanA$ is $\frac{2}{5}$.
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Important Questions from Trigonometric Ratios and Identities
The value of 4 sin 230° + 3 cot 260° - 2 tan 245° is:
The value of 1 - sin 35° cos 55° is equal to:
If sin 3 θ = cos ( θ – 6°), then θ is:
If θ = 45°, then what will be the value of \(\frac{{\\sin \,\theta \, + \,\cos \,\theta }}{{\sin \,\theta \, - \,\cos \,\theta }}\) ?
If sin A = \(\frac{1}{2}\) and cos B = \(\frac{1}{2}\) then find A + B.
