Question

31. (cot A - cosec A)2 =
1-cos A/1+COS A​

Answer 1

Answer:

Step-by-step explanation:

(cot A - cosec A)² =1-cos A / 1+cos A​

LHS=( cosA/sinA-1/sinA)²

=1/sin²A * ( cosA-1)²

=(1-cosA)²/(1-cos²A)

=(1-cosA)²/(1-cosA)(1+cosA)

=(1-cosA)/ (1+cosA)=RHS

Answer 2

Answer:

Start from the right-hand side. It's much easier. For the explanation, it has been lengthy. Ones you know it, then it's the easiest

Step-by-step explanation:

$\begin{aligned}R.H.S &=\frac{(1-\cos A)\times (1-\cos A)}{(1+\cos A) \times (1-\cos A)}\\&= \frac{(1-\cos A)^2} {1-\cos^2 A}\\&= \frac{(1-\cos A)^2}{\sin^2 A}\\&= \small (\frac{1-\cos A}{\sin A})\\&= (cosec A -\cot A)^2\\&= (\cot A - cosec A)^2\\&=L.H.S \end{aligned}$