Verify this triganomic identity you can only use 1 side to solve cos⁡x−tan⁡xsin⁡x+cos⁡x=cos⁡x−sec⁡x

First we need to check the identity. Let x=0 then: 1−00+1=1−1, which isn’t true because 1≠0, so the identity is false. To confirm, let x=π4: 22−1s2=22, 1−22≠−22 Therefore the identity has been wrongly stated. So the identity is actually an equation which has particular solutions for x. An identity has to be true for all x.

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High School
Geometry
Trigonometry
Trigonometric equations and identities

banganX

Answered question

2021-01-19

Verify this triganomic identity you can only use 1 side to solve

\frac{\cos x - \tan x}{\sin x + \cos x} = \cos x - \sec x

Answer & Explanation

gotovub

Skilled2021-01-20Added 98 answers

First we need to check the identity. Let x=0 then:
$\frac{1 - 0}{0 + 1} = 1 - 1$ , which isn’t true because $1 \neq 0$ , so the identity is false.
To confirm, let $x = \frac{π}{4} :$
$\frac{\frac{\sqrt{2}}{2} - 1}{s} \sqrt{2} = \frac{\sqrt{2}}{2}, \frac{1 - \sqrt{2}}{2} \neq - \frac{\sqrt{2}}{2}$
Therefore the identity has been wrongly stated. So the identity is actually an equation which has particular solutions for x. An identity has to be true for all x.

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