Question

Evaluate : sin 30° + cos 30° + tan 30° + cot 30° + sec 30° + cosec 30°

Answer 1

$\frac{1}{2} + \frac{ \sqrt{3} }{2} + \frac{1}{ \sqrt{3} } + \sqrt{3} + \frac{2}{ \sqrt{3} } + 2 \\ \frac{1 + \sqrt{3} }{2} + \frac{3}{ \sqrt{3} } + \sqrt{3} + 2 \\ \frac{1 + \sqrt{3} }{2} + \frac{ \sqrt{3} \times \sqrt{3} }{ \sqrt{3} } + \sqrt{3} + 2 \\ \frac{1 + \sqrt{3} }{2} + 2 \sqrt{3} + 2 \\ \frac{1 + \sqrt{3} }{2} + 2( \sqrt{3} + 1) \\ \frac{1 + \sqrt{3} + 4 \sqrt{3} + 4}{2} \\ \frac{5 + 5 \sqrt{3} }{2}$

hope this will help u

Answer 2

$\sin 30^\circ + \cos 30^\circ + \tan 30^\circ+ \cot 30^\circ+ \sec 30^\circ+ \csc 30^\circ=\frac{15+14\sqrt3}{6}$

Step-by-step explanation:

Given : Expression $\sin 30^\circ + \cos 30^\circ + \tan 30^\circ+ \cot 30^\circ+ \sec 30^\circ+ \csc 30^\circ$

To find : Evaluate the expression ?

Solution :

Expression $\sin 30^\circ + \cos 30^\circ + \tan 30^\circ+ \cot 30^\circ+ \sec 30^\circ+ \csc 30^\circ$

Using trigonometric values,

$\sin 30^\circ=\frac{1}{2}$

$\cos 30^\circ=\frac{\sqrt3}{2}$

$\tan 30^\circ=\frac{\sqrt 3}{3}$

$\csc 30^\circ=2$

$\sec 30^\circ=\frac{2\sqrt 3}{3}$

$\cot 30^\circ=\sqrt 3$

Substitute the values,

$=\frac{1}{2} +\frac{\sqrt3}{2} +\frac{\sqrt 3}{3}+ \sqrt 3+\frac{2\sqrt 3}{3}+2$

$=\frac{3+3\sqrt3+\sqrt 3+6\sqrt 3+4\sqrt 3+12}{2\times 3}$

$=\frac{15+14\sqrt3}{6}$

Therefore, $\sin 30^\circ + \cos 30^\circ + \tan 30^\circ+ \cot 30^\circ+ \sec 30^\circ+ \csc 30^\circ=\frac{15+14\sqrt3}{6}$

#Learn more

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