Question

square root of 1-cos^2 30/1-sin ^ 2 30​

Answer 1

Answer:

1-cos^2 30/1-sin^2 30

Step-by-step explanation:

√sin^2 30/√cos^2 30 = sin 30/cos 30=tan 30= 1/√3

Answer 2

Answer:

We can solve this question using trigonometric formula.

Final Answer: $\sqrt{\frac{1-cos^2 (30\textdegree)}{1-sin^2 (30\textdegree)} }=\frac{1}{\sqrt{3} }$

Step-by-step explanation:

The given question is,  $\sqrt{\frac{1-cos^2 (30\textdegree)}{1-sin^2 (30\textdegree)} }$

• In this question, numerator is equal to $1-cos^2\theta$ and the denominator is equal to $1-sin^2\theta$.
• Already we know the formula in trigonometric is,

                    $sin^2\theta+cos^2\theta=1$

• From this formula, $1-cos^2\theta = sin^2\theta$ and $1-sin^2\theta=cos^2\theta$
• Now apply the above formula in the given question.
• That is,    $\sqrt{\frac{1-cos^2 (30\textdegree)}{1-sin^2 (30\textdegree)} }=\sqrt{\frac{sin^2 (30\textdegree)}{cos^2 (30\textdegree)} }$

                                           $=\sqrt{\frac{sin (30\textdegree)^2}{cos(30\textdegree)^2} }$

                                           $=\sqrt{(\frac{sin (30\textdegree)}{cos(30\textdegree)})^2 }$

• Square root can be written in the following form.

                                           $={(\frac{sin (30\textdegree)}{cos(30\textdegree)})^{\frac{1}{2}* 2 }$  

                                           $=\frac{sin (30\textdegree)}{cos(30\textdegree)} }$

• Trigonometric formula, $\frac{sin\theta}{cos\theta} = tan\theta$. So that, the above equation is,

                               $\frac{sin (30\textdegree)}{cos(30\textdegree)} }=tan30\textdegree$

• From trigonometric table $tan 30\textdegree=\frac{1}{\sqrt{3} }$
• Final Answer : $\sqrt{\frac{1-cos^2 (30\textdegree)}{1-sin^2 (30\textdegree)} }=\frac{1}{\sqrt{3} }$