Question

find the value of sin60°+cos30°-tan 30°

Answer 1

sin60=√3/2,cos30=√3/2,tan30=1/√3

√3/2+√3/2-1/√3

2√3/2-1/√3

(√3(2√3)-2)/2√3                       -(cross multiplication)

(2×3-2)/2√3                                      -(√3×√3=3)

4/2√3                                            

(4/2√3)×(2√3 /2√3)                              -(rationalising denominator)

8√3/4×3                                                  -(√3×√3=3)

8√3/12

2√3/3

Answer 2

Hey there !

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We know that,

Value of Sin 60° = √3 / 2

Value of Cos 30° = √3 / 2

Value of Tan 30° = 1 / √3

So,

On substituting the values in

Sin 60° + Cos 30° - tan 30°

$\frac{ \sqrt{3} }{2} + \frac{ \sqrt{3} }{2} - \frac{1}{ \sqrt{3} } \\ \\ \frac{3 + 3 - 2}{2 \sqrt{3} } \\ \\ \frac{6 - 2}{2 \sqrt{3} } \\ \\ \frac{ \cancel 4 \: {}^{2} }{ \cancel 2 \sqrt{3} } \\ \\ \boxed{ \bold{ \frac{2}{ \sqrt{3} } }}$

Hence, the value is found.

And the answer is 2 / √3.

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Thanks for the question!