Question

Without using tables calculate 1+tan 60• tan 30• ➗ tan 60• + tan 30• what is the answer

Answer 1

Answer:

(1 + tan 60 * tan 30) / (tan 60 + tan 30) = (1 + cot 30 * tan 30) / (cot 30 + tan 30)

= (1 + (cos 30 / sin 30) * (sin 30 / cos 30))  / (cot 30 + tan 30)

= 2 /  (cot 30 + tan 30)

cot 30 + tan 30 = cos 30 / sin 30 + sin 30 / cos 30

= cos^2 30 / (sin 30 * cos 30) + sin^2 30 / (sin 30 cos 30)

= 1 / (sin 30 cos 30)      since cos^2 30 + sin^2 30 = 1

So we now have 2 * (sin 30 * cos 30)

and you can use sin 30 = 1/2 and cos 30 = 3^1/2 / 2