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