Question

sec 16 degrees cosec 74 degrees - cot 74 degrees tan 16 degrees​

Answer 1

Step-by-step explanation:

sec 16 degrees cosec 74 degrees - cot 74 degrees tan 16 degrees

= sec 16° cosec 74° - cot 74° tan 16°

= sec16° cosec(90°-16°) - cot(90°-16°) tan 16°

= sec 16° sec 16° - tan 16° tan 16°

= sec²16° - tan²16°

= 1 [ using identity sec²α - tan²α = 1 ]

Answer 2

$Sec16^o.Cosec74^o - Cot74^o.Tan16^o$

$Now, CosecA=Sec(90-A), CotA=Tan(90-A)$

=> $Sec(90-74)^o.Sec16^o-Tan(90-74)^o.Tan16^o$

=> $Sec16^o.Sec16^o-Tan16^o.Tan16^o$

=> $Sec^216^o-Tan^216^o$

$Now, Sec^2A-Tan^2A =1$

=> $Sec^216^o-Tan^216^o=1$

$Hence, Sec16^o.Cosec74^o - Cot74^o.Tan16^o=1$

Hope it helps.