Question

Prove: (tanx+tany)/(cotx+coty)=tanxtany

Answer 1

The easiest way is to go from the RHS.

Answer 2

Look at the LHS, what is the denominator?

Answer 3

cotx+coty

Answer 4

yup,
So, multiple the RHS by it, and divided by it as well. What do you have?

Answer 5

tanxtany(cotx+coty)/cotx+coty?

Answer 6

Good, keep the denominator as it is. Distribute the numerator. what do you get?

Answer 7

(tanxtanycotx+tanxtanycoty)/cotx+coty

Answer 8

So, you are done. Because tanx * cot x =1
Same as tan y* cot y =1

Answer 9

You get the LHS, right?

Answer 10

Ah!! Yes! Thank you so much!!!!!

Answer 11

np