Question

sin alpha.sin beta - cos alpha.cos beta+1=0 then prove that cot alpha.tan beta= -1​

Answer 1

Step-by-step explanation:

$Sin\alpha*Sin\beta-Cos\alpha*Cos\beta+1=0$

$Cos\alpha*Cos\beta-Sin\alpha*Sin\beta=1$

$Cos(\alpha + \beta)=1$

$Cos(\alpha + \beta)=Cos0$

$(\alpha + \beta) = 0$

$\beta = -\alpha$

$tan\beta= -tan\alpha$

$\frac{tan\beta}{tan\alpha}=-1$

$Cot\alpha*tan\beta = -1$