Question

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

Answer 1

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

$tan45=sin45/cos45=1$

$sin30=sin(\frac{\pi }{2}-60 )=cos60=\frac{1}{2}$

$cot45=cos45/sin45=1$

$sec60=1/cos60=\frac{1}{1/2} =2$

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

$(tan45.sin30)-(cot45/sec60)=(1.\frac{1}{2})-(\frac{1}{2} )=0$

Answer 2

Answer:

0

Step-by-step explanation:

Using trigonometric functions and table to substitute values,we obtain

• $1 \times \sin45 - \cfrac{ \cot(45) }{ \sec(60) }$

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

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

Rewrite 1/cos(60) as

• $\cfrac{1}{2} - \cfrac{ \cos(45) \times \cos(60) }{ \sin(45) }$

Rewriting again:

• $\cfrac{1}{2} - \cfrac{ \cancel{\cfrac{\sqrt{2}}{2} }\times \cfrac{1}{2} }{ \cancel{\cfrac{ \sqrt{2} }{2}} }$

• $\cfrac{1}{2} - \cfrac{1}{2}$

[LCM of 2 is 2]

• $\cfrac{1 - 1}{2} = \boxed0$