Question

​​​a+b=π/2

b+c=a

tan a=__________

1. 2(tan b+tan c)

2. tan b+tan c

3. tan b+2.tan c

4. 2.tan b+tan c

Answer 1

Solution: It is given in the question that A + B = π /2 and B + C = A.

Hence, A = π /2 – B

So, tan A = tan (π /2 – B) which gives tan A = cot B

Now, tan Atan B = 1

Also, B + C = A

So, C = A – B

tan C = tan (A – B)

also, tan C = (tan A – tanB)/ (1 + tan A tan B)

tan C = (tan A – tanB)/ (1 + 1)

Therefore, 2 tan C = tan A – tan B

Hence, tan A =tanB + 2 tan C