Question

If sin( A + 2B) = √3/2 and cos( A + 4B) = 0, then A+B=​

Answer 1

Answer:

45°

Step-by-step explanation:

$\sin(a + 2b) = \frac{ \sqrt{3} }{2} \\ \sin(60) = \frac{ \sqrt{3} }{2} \\ so \: a + 2b = 60 \: > > equation \: 1$

$\cos(a + 4b) = 0 \\ \cos(90) = 0 \\ a + 4b = 90 \: > > equation \: 2$

equation 2 - equation 1

2b=30°

b=30/2=15°

substitute value of b in equation 1

a + 2(15°) = 60°

a + 30°. = 60°

a = 60°-30°

a = 30°

So A+B=30°+15°=45°