If sinα.sinβ - cosα.cosβ + 1 = 0,then the value of cotα.tanβ is

a.-1

b.0

c.1

d.none of these

it can be either 1 or -1 . 

Hi Menka,

Please note for cot(alpha)*tan(beta) to be defined, cos(beta) and sin(alpha) must not be equal to zero.

Based on the above conclusion from the question, we proceed as follows,

sin(alpha)*sin(beta) + 1 = cos(alpha)*cos(beta)

1. Write, 1 = sin^2 alpha + cos^2 alpha,

That would give, sin(alpha)*sin(beta) + sin^2 alpha = cos(alpha)cos(beta) - cos^2 alpha

Now that would give, cot(alpha) = cot [(alpha - beta)/2] ---------- (1) {apply sinC+sinD, and cosC-cosD formula and simplify}

2. Next write 1 = sin^2 beta + cos^2 beta,

That would give, by proceeding as above, tan(beta) = tan [(beta-alpha)/2] --------- (2)

Now (1)*(2), would give the value of cot(alpha)*tan(beta) as -1.

Hence Option (A).

Hope that helps.

All the best,

Regards,

Ashwin (IIT Madras).

the answer is a.cos(a+b)=1

there fore a+b=o

cota=-cotb

cota*tanb=-1