Question

what is value of 'A'

the answer is 30° and 150°....
plzzz...don't spam....and explanation must...​

Answer 1

Step-by-step explanation:

Given,

$\cos^{2} ( \alpha ) - \sin( \alpha ) = \frac{1}{4}$

multiplying both side by 4, we get,

$4 \cos^{2} ( \alpha ) - 4 \sin( \alpha ) = 1$

$= 4(1 - \sin^{2} ( \alpha )) - 4 \sin( \alpha ) - 1 = 0$

$= 4 - 4 \sin^{2} ( \alpha ) - 4 \sin( \alpha ) - 1 = 0$

Taking minus common and simplying,we get,

$4 \sin^{2} ( \alpha ) + 4 \sin( \alpha ) - 3 = 0$

$4 \sin^{2} ( \alpha ) + 6 \sin( \alpha ) - 2 \sin( \alpha ) - 3 = 0$

$= 2 \sin( \alpha ) (2 \sin( \alpha ) + 3) - 1(2 \sin( \alpha ) + 3) = 0$

$= (2 \sin( \alpha ) + 3)(2 \sin( \alpha ) - 1) = 0$

$either \: \: (2 \sin( \alpha ) + 3) = 0 \: \: or \: \: (2 \sin( \alpha ) - 1) = 0$

$either \: \: \sin( \alpha ) = - \frac{3}{2} \: \: or \: \: \sin( \alpha ) = \frac{1}{2}$

we know that, sin(θ)€[-1,1], so, sin(θ) can not equals to -3/2, i.e., -1.5

so,

$\sin( \alpha ) = \frac{1}{2}$

$= \alpha = \frac{\pi}{6}$

i.e, α=30 degree