Answer:
![Sin (x) =\frac { 1} { Cos (x) - 1}](https://tex.z-dn.net/?f=Sin%20%28x%29%20%20%3D%5Cfrac%20%7B%201%7D%20%7B%20%20Cos%20%28x%29%20%20-%201%7D)
Step-by-step explanation:
Here, given :
sin 2 x - 2 sin x = 2 .... (1)
Now, by <u>TRIGONOMETRIC IDENTITY</u>:
Sin 2Ф = 2 SinФ CosФ
⇒ sin 2 x = 2 sin x cos x
Putting back the value in (1), we get:
sin 2 x - 2 sin x = 2 ⇒ (2 sin x cos x) - 2 sin x = 2
or, 2( sin x cos x - sin x) = 2
or, sin x cos x - sin x = 1
or, (sin x) ( cosx - 1) = 1
⇒ Sin x = 1 / ( Cos x - 1)
Hence, ![Sin (x) =\frac { 1} { Cos (x) - 1}](https://tex.z-dn.net/?f=Sin%20%28x%29%20%20%3D%5Cfrac%20%7B%201%7D%20%7B%20%20Cos%20%28x%29%20%20-%201%7D)
If 14 out of 20 is correct, then that is : 14/20 = 0.70 = 70%
It would be a combustion reaction
<u>Answer-</u>
<em>The distance d across the lake is </em><em>90ft.</em>
<u>Solution-</u>
In the picture,
ΔABC ≈ ΔCDE
Because,
- ∠ACB = ∠DCE (∵ vertical opposite angles)
- ∠B = ∠D = 90°
- ∠ACB = ∠CED (∵ as other two angles are same and sum of those two angles when subtracted from 180° will result the same)
So, from similarity properties
![\Rightarrow \dfrac{AB}{DE}=\dfrac{BC}{DC}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cdfrac%7BAB%7D%7BDE%7D%3D%5Cdfrac%7BBC%7D%7BDC%7D)
![\Rightarrow \dfrac{120}{20}=\dfrac{d}{15}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cdfrac%7B120%7D%7B20%7D%3D%5Cdfrac%7Bd%7D%7B15%7D)
![\Rightarrow d=\dfrac{120\times 15}{20}=90](https://tex.z-dn.net/?f=%5CRightarrow%20d%3D%5Cdfrac%7B120%5Ctimes%2015%7D%7B20%7D%3D90)