Question

1) (-tg35°-tg10°)/(tg35°tg10°-1) 2) (tg10°-tg35°)/(tg10°tg35°+1)

Answer 1

1) -( tg 35° + tg 10°)/ (-1 + tg 35°tg10°) = (tg35°+ tg10°) /(1-tg35° tg10°) = tg (35°+10°) = tg 45° = 1
2) (tg10°-tg35°) /(1+tg10° tg35°) = tg (10°-35°) = tg (-25°) = - tg 25°

Answer 2

Let's simplify these trigonometric expressions using some trigonometric identities:

1. (-tg35°-tg10°)/(tg35°tg10°-1)

We can rewrite -tg35° as -tan(45°-10°) and use the identity tan(a-b)=(tan(a)-tan(b))/(1+tan(a)tan(b)) to simplify the expression as follows:

(-tg35°-tg10°)/(tg35°tg10°-1) = (-tan(45°-10°)-tan(10°))/(tan(45°-10°)tan(10°)-1)

= [tan(10°)-tan(35°)]/[1-tan(10°)tan(35°)]

2. (tg10°-tg35°)/(tg10°tg35°+1)

We can rewrite -tg35° as -tan(45°+10°) and use the identity tan(a+b)=(tan(a)+tan(b))/(1-tan(a)tan(b)) to simplify the expression as follows:

(tg10°-tg35°)/(tg10°tg35°+1) = (tan(10°)-tan(45°+10°))/(tan(10°)tan(45°+10°)+1)

= [tan(10°)-(-tan(35°))]/[1-tan(10°)(-tan(35°))]

= [tan(10°)+tan(35°)]/[1+tan(10°)tan(35°)]

Therefore, the simplified expressions are:

1. [tan(10°)-tan(35°)]/[1-tan(10°)tan(35°)]

2. [tan(10°)+tan(35°)]/[1+tan(10°)tan(35°)]