Prove x - n- -1 n -2 or x - n -3 -4- where m - n - I

The given equation becomes (sin x 1)(sin x +cos x)=0 ⇒ sin x =1 or tan x = 1 ⇒ sin x =sin π/2 or tan x =tan 3 π/4 ⇒ x =n π+( 1)^n π/2 or x =m π +3 π/4, wh ...

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Standard XI

Mathematics

Sin2a and Cos2a in Terms of Tana

Prove x = nπ ...

Question

Prove $x = n π + (- 1)^{n} . \frac{π}{2}$ or $x = (n π + \frac{3 π}{4})$ , where m, $n \in I$

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Solution

The given equation becomes

(sin x -1)(sin x +cos x)=0

$\Rightarrow s i n x = 1$ or tan x =-1

$\Rightarrow s i n x = s i n \frac{π}{2}$ or $t a n x = t a n \frac{3 π}{4}$

$\Rightarrow x = n π + (- 1)^{n} \frac{π}{2}$ or $x = m π + \frac{3 π}{4}$ , where m, $n \in I .$

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Prove x=nπ+(−1)n.π2 or x=(nπ+3π4), where m, n∈I

The given equation becomes (sin x -1)(sin x +cos x)=0 ⇒ sin x=1 or tan x =-1 ⇒sin x=sin π2 or tan x=tan3π4 ⇒x=nπ+(−1)nπ2 or x=mπ+3π4, where m, n∈I.

Prove $x = n π + (- 1)^{n} . \frac{π}{2}$ or $x = (n π + \frac{3 π}{4})$ , where m, $n \in I$

The given equation becomes

(sin x -1)(sin x +cos x)=0

$\Rightarrow s i n x = 1$ or tan x =-1

$\Rightarrow s i n x = s i n \frac{π}{2}$ or $t a n x = t a n \frac{3 π}{4}$

$\Rightarrow x = n π + (- 1)^{n} \frac{π}{2}$ or $x = m π + \frac{3 π}{4}$ , where m, $n \in I .$