Question

Find all solutions to the equation. 7 sin2x - 14 sin x 2 = -5

Answer 1

Answer:

The all solution of given trigonometrical equation is $\frac{\Pi }{2}$ + 2πn   .

Step-by-step explanation:

Given trigonometrical equation as :

7 $sin^{2}x$ - 14 sin x + 2 = - 5

Now, Rearranging the equation

7 $sin^{2}x$ - 14 sin x + 2 + 5 = 0

Or, 7 $sin^{2}x$ - 14 sin x + 7 = 0.

Taking 7 as common

So,  $sin^{2}x$ - 2 sin x + 1 = 0.

∵The standard form of quadratic equation

a x² + b x + c = 0

So, breaking the mid term we get

$sin^{2}x$ - 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 = $sin^{-1}1$

i.e x = 90°

Or, ∠x = $\frac{\Pi }{2}$

And for all solution $\frac{\Pi }{2}$ + 2πn  , where n∈ 0  to ....

Hence, The all solution of given trigonometrical equation is $\frac{\Pi }{2}$ + 2πn   . Answer