We have, √(2) sec x + tan x= 1 ⇒ √(2)/cos x + sin x/cos x=1 ⇒ √(2)+sin x = cos x ⇒ cos x sin x = √(2) On dividing both sides by √(2), we get 1/√(2) cos ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Mathematics

General Solution of Cos theta = Cos alpha

Solve √2 x+ta...

Question

Solve $\sqrt{2} s e c x + t a n x = 1$

Open in App

Solution

We have, $\sqrt{2} s e c x + t a n x = 1$

$\Rightarrow \frac{\sqrt{2}}{c o s x} + \frac{s i n x}{c o s x} = 1$

$\Rightarrow \sqrt{2} + s i n x = c o s x$

$\Rightarrow c o s x - s i n x = \sqrt{2}$

On dividing both sides by $\sqrt{2}$ , we get

$\frac{1}{\sqrt{2}} c o s x - \frac{1}{\sqrt{2}} s i n x = \frac{\sqrt{2}}{\sqrt{2}}$

$\Rightarrow c o s \frac{π}{4} c o s x - s i n \frac{π}{4} s i n x = 1$

$\Rightarrow c o s (x + \frac{π}{4}) = 1$

$[∵ c o s (A + B) = c o s A c o s B - s i n A s i n B]$

$\Rightarrow c o s (x + \frac{π}{4}) = c o s 0^{\circ}$

$\Rightarrow x + \frac{π}{4} = 2 n π \pm 0, n ϵ Z$

$∴ x = 2 n π - \frac{π}{4}, n ϵ Z$

Suggest Corrections

Similar questions

Q. Solve

\int e^{x} (\frac{2 tan x}{1 + tan x} + {cot}^{2} (x + \frac{π}{4})) d x

Solve $lim x \to \frac{π}{2} (sec x - tan x)$

Q. Solve:

\frac{1}{tan x} - 1 = \frac{cos 2 x}{1 + tan x} .

Q. Solve

\frac{1 + tan x}{1 - tan x} = (sin x + cos x)^{2} .

Q. Solve

tan x = \frac{1}{\sqrt{3}}

Join BYJU'S Learning Program

Solve √2sec x+tan x=1

Solve $\sqrt{2} s e c x + t a n x = 1$