96 points here, having to ask same question again - please help a brother out.

Mathematics

2 answers:

Sauron [17]2 years ago

7 0

See attached pictures for answers

marin [14]2 years ago

3 0

the equation is - tan2 x + sec2 x = 1.

Left hand side identity : - tan2 x + sec2 x.

Trigonometric function : tan x = sin x / cos x,

Reciprocal identity : sec x = 1/cos x.

- tan2 x + sec2 x = - (sin x/cos x)2 + (1/cos x)2

= - sin2 x/cos2 x + 1/cos2 x

= (1 - sin2 x)/cos2 x

Pythagorean identity : sin2 x + cos2 x = 1 .

= cos2 x / cos2 x

= 1

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Prove identity trigonometric equation

irina [24]

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$2\tan{x}=\dfrac{\cos{x}}{\csc{(x)}-1}+\dfrac{\cos{x}}{\csc{(x)}+1}$

This is one way to show it:

$2\tan{x}=\cos{(x)}\dfrac{(\csc{(x)}+1)+(\csc{(x)}-1)}{(\csc{(x)}-1)(\csc{(x)}+1)}\\\\=\cos{(x)}\dfrac{2\csc{(x)}}{\csc{(x)}^2-1}=2\cos{(x)}\dfrac{\csc{x}}{\cot{(x)}^2}=2\dfrac{\cos{(x)}\sin{(x)}^2}{\cos{(x)}^2\sin{(x)}}\\\\=2\dfrac{\sin{x}}{\cos{x}}\\\\2\tan{x}=2\tan{x}\qquad\text{QED}$