Question

find all the trigonometric ratios for the following triangle​

Answer 1

$\underline{\textsf{To find:}}$

$\textsf{All trigonometric ratios of the given angle}$

$\underline{\textsf{Solution:}}$

$\textsf{Here,}$

$\textsf{Opposite side=x}$

$\textsf{Adjacent side=x}$

$\textsf{Hypotenuse}\mathsf{=\sqrt{2}x}$

$\mathsf{sin\,45^{\circ}=\dfrac{\textsf{Opposite side}}{\textsf{Hypotenuse}}=\dfrac{x}{\sqrt{2}x}=\dfrac{1}{\sqrt{2}}}$

$\mathsf{cos\,45^{\circ}=\dfrac{\textsf{Adjacent side}}{\textsf{Hypotenuse}}=\dfrac{x}{\sqrt{2}x}=\dfrac{1}{\sqrt{2}}}$

$\mathsf{tan\,45^{\circ}=\dfrac{\textsf{Opposite side}}{\textsf{Adjacent side}}=\dfrac{x}{x}=1}$

$\mathsf{cosec\,45^{\circ}=\dfrac{\textsf{Hypotenuse}}{\textsf{Opposite side}}=\dfrac{\sqrt{2}x}{x}=\sqrt{2}}$

$\mathsf{sec\,45^{\circ}=\dfrac{\textsf{Hypotenuse}}{\textsf{Adjacent side}}=\dfrac{\sqrt{2}x}{x}=\sqrt{2}}$

$\mathsf{cot\,45^{\circ}=\dfrac{\textsf{Adjacent side}}{\textsf{Opposite side}}=\dfrac{x}{x}=1}$