Question

find the value of :2 cos 67°/sin23°+4 cot 45°​

Answer 1

Given :

An expression $2\frac{cos67}{sin23} +4cot45$

To find :

The value of the given expression.

Step-by-step explanation:

• We know that, the sine will change into cosine after the angles gets subtracted from $90$°.
• The cosine can we written in terms of sin.
• Then the equation will become

        $cosx=sin(90-x)$

• $67$ is $23$ when subtracted from $90$

• In this case, the equation will become      

        $2\frac{cos(90-23)}{sin23} +4cot45$

• Sine will change into cosine when the angles are subtracted from $90$.
• Then the equation will become

         $2\frac{sin23}{sin23} +4cot45$

• The sign will remain as positive because sine is positive in the first quadrant.
• Cancel out the like terms.
• This equation will become

         $2(1)+4cot45$

• Remove the brackets

         $2+4cot45$

• We know that the value of $cot45$ is $1$
• Substitute the value in the given equation

         $2+4(1)$

• Sum it all up.

         $6$

Final answer :

The value of $2\frac{cos67}{sin23} +4cot45$ is $6$.