$\frac{2}{5}$
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
If cosec θ = 13/12, then sin θ + cos θ - tan θ is equal to:
What is the value of \(\frac{3 \sin 58^{\circ}}{\cos 32^{\circ}}+\frac{3 \sin 42^{\circ}}{\cos 48^{\circ}}\) ?
If \(\frac{{\tan \theta + \sin \theta }}{{\tan \theta - \sin \theta }} = \frac{{k + 1}}{{k - 1}},\) then k = ?
If α + β = 90° and α = 2β, then the value of 3 cos 2 α - 2 sin 2 β is equal to:
If \(\sqrt{3}\) tan θ = 3 sin θ, then what is the value of sin 2θ − cos 2θ ?
