Question

Root 3 sinA-cosA=root 2 .find the value of angle A

Answer 1

$\huge\tt{\red{GIVEN}}$:

★$\sqrt{3}sinA - cosA=\sqrt{2}$

$\huge\tt{\red{TO\:\: FIND}}$:

★The value of angle A .

$\huge\tt{\red{CONCEPT \:\:USED}}$:

★We would be using the concept of Compound angles

$\huge\tt{\red{ANSWER}}$:

We have,

=> $\sqrt{3}sinA - cosA=\sqrt{2}$

Multiplying both sides by $\dfrac{1}{2}$

=>$\dfrac{1}{2}(\sqrt{3}sinA - cosA) =\dfrac{1}{2}\sqrt{2}$

=>$\dfrac{\sqrt{3}}{2}sinA-\dfrac{1}{2}cosA=\dfrac{\sqrt{2}}{2}$

=>$sin60°sinA -cos60° cosA=\dfrac{\sqrt{2}}{\sqrt{2}×\sqrt{2}}$

$\large\green{\boxed{sin60°=\dfrac{\sqrt{3}}{2}}}$

$\large\red{\boxed{cos60°=\dfrac{1}{2}}}$

=>$sin(60°-A) =\dfrac{1}{\sqrt{2}}$

$\large\purple{\boxed{sin(A-B) =sinAcosB - cosA sinB}}$

=>$sin(60°-A) =sin45°$

=>$60°-A = 45°$

=>$A = 60°-45°$

. °. $A = 15°$

Therefore the value of the angle A is 15°.

$\huge\orange{\boxed{.°.A =15°}}$