Show that cot ø+ tanø= secø x cosecø
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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) ⇒ (cot Ø+ cosec Ø ) ⇒ (cos Ø+1)/sin Ø.
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