Question

If A and B are acute angles such that SinA/SinB=√2 and tanA/tanB=√3. then find angle A and angle B please give me d ans as soon as possible ......

Answer 1

sinA/sinB=√2
or, sinA=√2sinB
or, sin²A=2sin²B
∴, cos²A=(1-sin²A) [∵, sin²A+cos²A=1]
or, cos²A=1-2sin²B
∴, tanA/tanB=√3
or, tan²A/tan²B=3
or, (sin²A/cos²A)/(sin²B/cos²B)=3
or, 2sin²B/1-2sin²B×cos²B/sin²B=3
or, 2cos²B/(1-2sin²B)=3
or, 2cos²B=3-6sin²B
or, 2(1-sin²B)=3-6sin²B
or, -2sin²B+6sin²B=3-2
or, 4sin²B=1
or, sin²B=1/4
or, sinB=1/2 [∵, B is an acute angle]
∴, sinB=sin30°
or, B=30° and
sinA=√2sinB
or, sinA=√2sin30°
or, sinA=√2×1/2
or, sinA=1/√2
or, sinA=sin45°
or, A=45°
∴, A=45°, B=30°