If x, y are acute angles, 0 < x + y < 90° and sin(2x - 20°) = cos(2y + 20°), then the value of tan(x + y) is?

Question

নিচের অপশন গুলা দেখুন

• $$\frac{{\sqrt 3 }}{2}$$
• $$\frac{1}{{\sqrt 3 }}$$
• $$\sqrt 3 $$
• 1

Answer 1

সঠিক উত্তর হচ্ছে: 1

ব্যাখ্যা:

$$\eqalign{ & {\text{sin}}\left( {2x - {{20}^ \circ }} \right) = {\text{cos}}\left( {2y + {{20}^ \circ }} \right) \cr & \Rightarrow \left( {2x - {{20}^ \circ }} \right) + \left( {2y + {{20}^ \circ }} \right) = {90^ \circ } \cr & \left[ {{\text{If sin A}} = {\text{cos B, then A}} + {\text{B}} = {{90}^ \circ }} \right] \cr & \Rightarrow 2\left( {x + y} \right) = {90^ \circ } \cr & \Rightarrow x + y = {45^ \circ } \cr & \therefore \tan \left( {x + y} \right) \cr & = \tan {45^ \circ } \cr & = 1 \cr} $$