Question

Find the value of tan135+sin240+cot420

Answer 1

Answer:

(-1-2√3) / 2√3

Explanation:

tan 135 = tan (180-45) = -tan 45 = -1

sin 240 = sin (180+60) = -sin 60 = -√3/2

cot 420 = cot(360+60) = cot 60 = 1/√3

1/√3 - 1 - √3/2 = (-1-2√3) / 2√3

Answer 2

The correct answer is $\frac{-6+5\sqrt{3} }{6 }$.

Given: The equation =  tan135°+sin240°+cot420°.

To Find: The value of the equation.

Solution:

tan135°+sin240°+cot420°

Take first term tan135°.

tan135° = tan(180-45)° = -tan45° = -1

Take second term sin240°.

sin240° = sin(180+60)° = -sin60° = $\frac{-\sqrt{3} }{2}$.

Take second term cot420°.

cot420° = cot(360+60)° = cot60° = $\frac{1}{\sqrt{3} }$.

Put all the terms in equation.

= $-1-(\frac{-\sqrt{3} }{2}) +\frac{1}{\sqrt{3} }$

= $\frac{-2\sqrt{3}+3+2 }{2\sqrt{3} }$

= $\frac{-2\sqrt{3}+5 }{2\sqrt{3} }$

= $\frac{-2\sqrt{3}+5 }{2\sqrt{3} }*\frac{\sqrt{3} }{\sqrt{3} }$

= $\frac{-6+5\sqrt{3} }{6 }$

Multiply and divide by $\sqrt{3}$ to rationalize the term.

Hence, the answer is $\frac{-6+5\sqrt{3} }{6 }$.

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