Question

Question
If sin A =1/2 - and sin B =1/√2 find:
tan A + tan B/1-tan A tan B.
​

Answer 1

Answer:

2 + root3

Step-by-step explanation:

sin A = 1/2, sin30 = 1/2, so A = 30 degrees

sin B = 1/root2, sin 45 = 1/root2, so B = 45 degrees

tan A = tan 30 = 1/root3

tan B = tan 45 = 1

so,

(tan A + tan B)/(1-tan A tan B)

= (1/root3+1) / (1- 1/root3)

= (1+ 1/root3)^2 / (1 - 1/3)

= (root3+1)^2 / 3    /  2/3

3 and 3 cancel,

= (3+1+2root3)/2

= (4+2root3)/2

= 2+root3

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