Question

Simply
tan 45°. sin 30° - cot 45°/sec 60°​

Answer 1

0

Explanation:

Using trigonometric functions and table to substitute values,we obtain

• 
  `1 * \sin45 - \cfrac{ \cot(45) }{ \sec(60) }`

• 
  `\sin(30) - \cfrac{ \cfrac{\cos(45)}{ \sin45} }{ \cfrac{1}{ \cos(60) } }`

• 
  `\cfrac{1}{2} - \cfrac{ \cfrac{\cos(45)}{ \sin45} }{ \cfrac{1}{ \cos(60) } }`

Rewrite 1/cos(60) as

• 
  `\cfrac{1}{2} - \cfrac{ \cos(45) * \cos(60) }{ \sin(45) }`

Rewriting again:

• 
  `\cfrac{1}{2} - \cfrac{ \cancel{\cfrac{√(2)}{2} }* \cfrac{1}{2} }{ \cancel{\cfrac{ √(2) }{2}} }`

• 
  `\cfrac{1}{2} - \cfrac{1}{2}`

[LCM of 2 is 2]

• 
  `\cfrac{1 - 1}{2} = \boxed0`

Answer 2

If we want to write the given four numbers in another form, we can write it like this;

`tan45=sin45/cos45=1`

`sin30=sin((\pi )/(2)-60 )=cos60=(1)/(2)`

`cot45=cos45/sin45=1`

`sec60=1/cos60=(1)/(1/2) =2`

Now let's rewrite the given expression and get the result.

`(tan45.sin30)-(cot45/sec60)=(1.(1)/(2))-((1)/(2) )=0`