Question

coseA+cotA+prove that msquare-1/msquare+1=cosA​

Answer 1

Solution

If coseca + cota = m

then , m²-1 / m²+1 = cosA

coseca + cot a. = m

1/sin a + cosA/sin a = m

Taking LCM

1+cos a/ sin a. = m

Squaring both sides we got

[(1+cosA)²/sin²a]. = m²

1+cos²a +2cos a / sin² a = m²

LHS

m²-1/ m²+1

Replacing m² with its above value we got

$\frac{ \frac{1 + { \cos(a) }^{2} + 2 \cos(a) }{ { \sin(a) }^{2} } - 1} { \frac{1 + { \cos(a) }^{2} + 2 \cos(a) } { { \sin(a) }^{2} } + 1 }$

Taking LCM

(1-sin²a +cos²a +2cosa /sin²a)/(1+sin²a +cos²a +2cosa )

2cos²a +2cosa / 2 cos a +2

2cos a( cosA +1 )/ 2 ( cosA +1 )

2cosa / 2

cosa

hence proved