Question

show this by your explanation
1+cos^2 a /sin^2 a = 2cosec a -1

Answer 1

Hey friend,

The question should be -
1 + cos^2A / sin^2A = 2 cosec^2A - 1

LHS
= 1/sin^2A + cos^2A/sin^2A       (splitting the numerator)
= cosec^2A + cot^2A                  (cotA = cosA/sinA)
= cosec^2A + cosec^2A - 1         (cot^2A = cosec^2A - 1)
= 2 cosec^2A - 1
=RHS

LHS = RHS
Hence Proved!

Hope it helps!

Answer 2

Hello friend

___________________________

Here is your answer!!!

Take L.H.S

$\frac{1 + cos {}^{2} a}{sin {}^{2}a } \\ \\ => \frac{1}{sin {}^{2}a \: } + \frac{cos {}^{2} a}{sin {}^{2} a}$

$=>cosec {}^{2} a + cot {}^{2} a \\ \\ =>cosec {}^{2} a \: + \: cosec {}^{2}a - 1 \\ \\=> 2cosec {}^{2} a \: - 1$

: L.H.S = R.H.S

We have proved...

Thanks..

:)