Question

Solve √2sec theta+tan theta=1

Answer 1

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Answer 2

Answer:

$\theta=2n\pi-\frac{\pi}{4}$

Step-by-step explanation:

Given : Expression $\sqrt 2\sec\theta+\tan \theta=1$

To find : Solve the expression ?

Solution :

Expression $\sqrt 2\sec\theta+\tan \theta=1$

$\sqrt 2\sec\theta=1-\tan \theta$

Squaring both side,

$(\sqrt 2\sec\theta)^2=(1-\tan \theta)^2$

$2\sec^2\theta=(1-\tan \theta)^2$

We know, $\sec^2\theta=1+\tan^2\theta$

$2+2\tan^2\theta=1+\tan^2\theta-2\tan\theta$

$\tan^2\theta+2\tan\theta+1=0$

$(\tan\theta+1)^2=0$

Squaring both side,

$\tan\theta+1=0$

$\tan\theta=-1$

$\tan\theta=\tan (2n\pi-\frac{\pi}{4})$

$\theta=2n\pi-\frac{\pi}{4}$

Therefore, $\theta=2n\pi-\frac{\pi}{4}$