Answer
Required trigonometric functions are-
$\sin A = \frac{1}{\sqrt 2}$
$\\csc A = \sqrt 2 $
$\\cos A = \frac{1}{\sqrt 2}$
$\\sec A = \sqrt 2 $
$\\tan A = 1$
$\\\cot A = 1$
Work Step by Step
Steps to Answer-
From the given diagram of triangle ABC, we will use given information and Pythagoras Theorem to solve for 'c'-
$c^{2} =a^{2} + b^{2}$ ( Pythagoras Theorem)
$c^{2} = x^{2} + x^{2}$
$c^{2} = 2 x^{2}$
therefore $ c = x \sqrt 2$
Now we can write the required six T-functions of A using a =$ x$, $b= x$ and $ c =x\sqrt 2$
$\sin A = \frac{a}{c} = \frac{x}{x\sqrt 2} = \frac{1}{\sqrt 2}$
$\\csc A = \frac{c}{a} =\frac{x\sqrt 2}{x} = \frac{\sqrt 2}{1} = \sqrt 2 $
$\\cos A = \frac{b}{c} = \frac{x}{x\sqrt 2} = \frac{1}{\sqrt 2}$
$\\sec A = \frac{c}{b} =\frac{x\sqrt 2}{x} = \frac{\sqrt 2}{1} = \sqrt 2 $
$\\tan A = \frac{a}{b} = \frac{x}{x} = 1$
$\\\cot A = \frac{b}{a} = \frac{x}{x} = 1$
