Question

(cosecø-cotø)²=1-cosø/1+cosø​

Answer 1

Hey mate,...

Sol : ⇒ (cot Ø+cosec Ø-1) / (cot Ø-cosec Ø+1 )

(rationalize numerator and denominator by)

(cotØ+1+cosecØ ) ⇒ (cot Ø+cosec Ø-1) (cot Ø+1+cosec Ø ) /(cot Ø+1-cosec Ø ) (cot Ø+1+cosec Ø )

∴ ((a-b)( a+b )= a2-b2 ) ⇒ (cot2 Ø+cosec2 Ø+ 2 cot Øcosec Ø-1 ) /(cot2 Ø +1 + 2 cot Ø-cosec2 Ø)

∴ (cosec2 Ø-1= cot2 Ø) ⇒ (2cot2 Ø+ 2 cot Ø cosec Ø ) / (2 cot Ø)

⇒ (2cot2 Ø+ 2 cot Øcosec Ø ) / (2 cot Ø)

⇒ 2 cot Ø (cot Ø+ cosec Ø ) / (2 cot Ø)

Hope it will help you.

⇒ (cot Ø+ cosec Ø ) ⇒ (cos Ø+1)/sin Ø.

Answer 2

Answer:

Step-by-step explanation:

\frac{1 + \cos( \alpha ) }{1 - \cos( \alpha ) } \times \frac{1 + \cos( \alpha ) }{1 + \cos( \alpha ) }

= {(1 + \cos( \alpha )) }^{2} \div (1 - { \cos( \alpha ) }^{2} )

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

= {( \frac{1}{ \sin( \alpha ) } + \frac{ \cos( \alpha ) }{ \sin( \alpha ) } )}^{2} \\ = {( \csc( \alpha) + \cot( \alpha ) ) }^{2}