Answer:
The all solution of given trigonometrical equation is
+ 2πn .
Step-by-step explanation:
Given trigonometrical equation as :
7
- 14 sin x + 2 = - 5
Now, Rearranging the equation
7
- 14 sin x + 2 + 5 = 0
Or, 7
- 14 sin x + 7 = 0.
Taking 7 as common
So,
- 2 sin x + 1 = 0.
∵The standard form of quadratic equation
a x² + b x + c = 0
So, breaking the mid term we get
- sin x - sin x + 1 = 0.
Or, sin x (sin x - 1) - 1 (sin x - 1) = 0
Or, (sin x - 1) (sin x - 1) = 0
Or, (sin x -1) = 0 and (sin x - 1) = 0
So, sin x = 1
∴ x = 
i.e x = 90°
Or, ∠x = 
And for all solution
+ 2πn , where n∈ 0 to ....
Hence, The all solution of given trigonometrical equation is
+ 2πn . Answer