Question

If sin A=1/2, then find the value of cos A.​

Answer 1

Given :

• Sin A = 1/2

To Find :

• Value of Cos A

Solution :

Use formula :

⇒Sin²A + Cos²A = 1

⇒(1/2)² + Cos²A = 1

⇒1/4 + Cos²A = 1

⇒Cos²A = 1 - 1/4

⇒Cos²A = (4 - 1)/4

⇒Cos²A = 3/4

⇒CosA = √(3/4)

⇒CosA = √3/2

$\rule{150}{0.5}$

⇒A = Cos^-1(√3/2)

⇒A = 30°

Answer 2

$\sf{\large{\bold{\pink{\bigstar{\boxed{\boxed{Question}}}}}}}$

• If sin A=$\dfrac{1}{2}$then find the value of cos A.

$\sf{\large{\bold{\pink{\bigstar{\boxed{\boxed{Solution}}}}}}}$

$\sf{\bold{\green{\underline{\underline{sin^2A + cos^2A = 1 }}}}}$

$\sf\implies (\dfrac{1}{2})^2 + cos ^2A = 1$

$\sf\implies \dfrac{1}{4}+ cos ^2A = 1$

$\sf\implies cos ^2A = 1 - \dfrac{1}{4}$

$\sf\implies cos ^2A = \dfrac{4 -1}{4}$

$\sf\implies cos ^2A = \dfrac{3}{4}$

$\sf\implies cos A =\sqrt{ \dfrac{3}{4}}$

$\sf\implies cos A = \dfrac{\sqrt 3}{2}$

$\sf{\bold{\green{\underline{\underline{Cos 30 = cos \dfrac{\sqrt 3}{2}}}}}}$

$\sf\implies cos A = cos 30$