Question

-1+sinA sin(90-A)/cot(90-A)= sin A

Answer 1

sin (90- A)= cos A

cot (90-A)= tan A


LHS = -1 + sin A sin(90-A)/cot(90-A)

= -1+ sinAcos A/tanA

= -1 + sinA cosA * cosA/sinA

= -1 + cos^2A
= -(1- cos^2 A)
= - sin^2 A

Answer 2

Answer:

To Prove : $-1+sinA \times \frac{sin(90-A)}{cot(90-A)}= sin^2 A$

Solution :

$-1+sinA \times \frac{sin(90-A)}{cot(90-A)}$

Using identities : $sin (90-\theta)= cos \theta\\cot(90-\theta)= tan \theta$

$-1+sinA \times \frac{CosA}{Tan A}$

$-1+sinA \times \frac{CosA}{\frac{SinA}{CosA}}$

$-1+cos^2 A$

$-(1-cos^2 A)$

Identity : $Sin^2 A +Cos^2 A = 1$

$-sin^2A$

Hence proved