Question

(1+4xsquare)cosA=4x then prove cosecA+cotA=1+2x/1-2x

Answer 1

$\cos(a) = \frac{4x}{1 + 4x {}^{2} }$
Now using cos^2(a)+sin^2(a)=1
we find
$\sin(a) = \frac{4x ^{2} - 1 }{4x {}^{2} + 1 }$
now we want
cosec a + cot a
=1/Sina +cosa /Sina
=(4x^2+1)/(4x^2-1) + 4x/(4x^2-1)
The denominator is common
so
=(4x^2+1+4x)/(4x^2-1)
=(2x+1)^2/(2x-1)(2x+1)
=(2x+1)/(2x-1)
The only difference is my answer is getting 2x-1 but the answer has 1-2x
so I would like u to check the question once again if I am wrong I would edit my answer
Ans the method is pretty much clear
HOPE IT HELPS
MARK AS BRAINLIEST