Q16 of 27 Page 301

If A and B are acute angles such that tan , show that A + B = 45°.

Given: tan (A +B) = and tan A = 1/3, tan B = 1/2


∴ tan(A +B) = = = = 1


∴ tan(A + B) = 1


Also, A and B are acute angles, therefore both A and B are less than 90°. So A + B must be less than 180°.


Therefore, the only possible case for which tan (A+B) = 1 will be when (A + B) equals 45°.


Thus, A + B = 45°


More from this chapter

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14

If A = 60° and B = 30°, verify that:

(i) sin (A + B) = sin A cos B + cos A sin B


(ii) cos (A + B) = cos A cos B — sin A sin B

 15

If A = 60° and B = 30°, verify that:

(i) sin (A — B) = sin A cos B — cos A sin B


(ii) cos (A — B) = cos A cos B + sin A sin B


(iii)

17

Using the formula, , find the value of tan 60°, it being given that

18

Using the formula,, find the value of cos 30°, it being given that cos 60° = 1/2 .