Question

If sin A =1/root10
sin B=1/root5
0<A, B < pie/4 then a+b=

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Answer 1

Answer:

sin(a+b)= sinacosb+ cosasinb

Sina =1/root10

cosa= 3/root10(from pythogreas rule)

sinb= 1/root5

cosb= 2/root5

sin(a+b)= sinpi/4

sin(a+b)= 1/root2

now sin(a+b)= 1/root10 * 2/root5 + 3/root10 * 1/root5

= 2/5root2 + 3/5 root2

= 5/ 5root2

= 1/root2

sin(a+b) = sinpi/4 = 1/root2

therefore a+b = pi/4 is proved