Question

${\mathbb{\huge{QUESTION\: :-}}}$

$if \: cos \: A \: + sin \: A \: = \frac{1}{2(cos \: A - sin \: A)} \\ \\(0 < A < 90) \\ \\ then \: find \: the \: value \: of \: {sin}^{2} A$

${\texttt{\large{Please help}}}$

^_^

Answer 1

hey mate

refer to attachment

Answer 2

Answer:

⇒ (1/4) (or) 30°.

Step-by-step explanation:

Given Equation is cos A + sinA = 1/2(cosA - sinA)

⇒ (cosA + sinA)(cosA + sinA) = (1/2)

⇒ cos²A - sin²A = (1/2)

⇒ (1 - sin²A) - sin²A = (1/2)

⇒ 1 - sin²A - sin²A = (1/2)

⇒ 1 - 2sin²A = (1/2)

⇒ -2sin²A = (1/2) - 1

⇒ -2sin²A = -1/2

⇒ sin²A = 1/4.

(or)

⇒ sinA = (1/2)

⇒ A = 30° {0 < A < 90°}

Therefore, sin² A = (1/4) and A = 30°.

Hope it helps!