Evaluate : (sec2 45° – tan2 45°)/sin2 45°

Q) Evaluate : (sec² 45⁰ – tan² 45⁰)/sin² 45⁰

Ans:

We know that: sec 45⁰ = $\sqrt 2$ , tan 45⁰ = 1, sin 45⁰ = $\frac{1}{\sqrt 2}$ ;

By submitting these values in the given expression, we get:

$\frac{sec^2 45 - tan ^2 45}{sin^2 45}$

= $\frac{(\sqrt 2)^2 - (1)^2}{(\frac{1}{\sqrt 2})^2}$

= $\frac{2 - 1}{\frac{1}{2}} = \frac{1}{\frac{1}{2}}$

= 1 x 2 = 2

Hence the value of the given function is 2.

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