Question

Cosec²ø+cot²ø= ?
Solve this

Answer 1

Given: a cot θ + b cosec θ = p
Squaring both sides, we get
(a cot θ + b cosec θ)2 = p2
⇒ a2 cot2 θ + b2 cosec2 θ + 2ab cot θ cosec θ = p2 ……(i)
and b cot θ + a cosec θ = q
Squaring both sides, we get
(b cot θ + a cosec θ)2 = q2
⇒ b2 cot2 θ + a2 cosec2 θ + 2ab cot θ cosec θ = q2 ……(ii)
To find: p2 – q2
Subtracting (ii) from (i), we get
a2 cot2 θ + b2 cosec2 θ + 2ab cot θ cosec θ – b2 cot2 θ – a2 cosec2 θ – 2ab cot θ cosec θ = p2 – q2
⇒ P2 – q2 = a2 (cot2 θ – cosec2 θ) + b2(cosec2 θ – cot2 θ)
= a2 ( – 1) + b2 (1) [∵1 = cosec2 θ – cot2 θ]
= b2 – a2

Answer 2

we have to find the value of :-


${ \csc( \alpha ) }^{2} + { \cot(?) }^{2} =$
we know,


$\csc( \alpha ) = \frac{1}{ \sin( \alpha ) }$
and,
$\cot( \alpha ) = \frac{ \cos( \alpha ) }{ \sin( \alpha ) }$

putting these values in expression given,

$\frac{1}{ { \sin( \alpha ) }^{2} } + \frac{ { \cos( \alpha ) }^{2} }{ { \sin( \alpha ) }^{2} }$
adding, we get

$\frac{1 + { \cos( \alpha ) }^{2} }{ { \sin( \alpha ) }^{2} }$
Answer