36^ = 10-2 5 4 - Vidyadip

Question

$\sin 36^{\circ}=\frac{\sqrt{10-2 \sqrt{5}}}{4}$

✓

Answer

We know that, $\sin ^2 \theta=1-\cos ^2 \theta$
$\begin{aligned}
& \sin ^2 36^{\circ}=1-\cos ^2 36^{\circ} \\
& =1-\left(\frac{\sqrt{5}+1}{4}\right)^2 \\
& =\frac{16-(5+1+2 \sqrt{5})}{16} \\
& =\frac{10-2 \sqrt{5}}{16} \\
& \therefore \sin 36^{\circ}=\frac{\sqrt{10-2 \sqrt{5}}}{4} \ldots \ldots\left[\because \sin 36^{\circ} \text { is positive }\right]
\end{aligned}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(2 Marks)" from Trigonometry – II→Trigonometry – II — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

Evaluate the following limits: $\lim _{x \rightarrow 0}\left[\frac{5 x+3}{3-2 x}\right]^{\frac{2}{x}}$

If ω is the complex cube root of unity, show that

$\frac{a+b w+c w^2}{c+a w+b w^2}=\omega^2$

The 6th and 17th terms of an A.P. are 19 and 41 respectively, find the 40th term.

If a is the G.M. of 2 and $\frac14,$ find a.

A Signal is generated from 2 flags by putting one flag above the other. If 4 flags of different colours are available, how many different signals can be generated?

Find the other trigonometric functions if : $\cot x=\frac{3}{4}$, $x$ lies in the third quadrant.

Write the relation in the Roster form. State its domain and range.

$R_4=\{(x, y) / y>x+1, x=1,2$ and $y=2,4,6\}$

Differentiate the following w.r.t. $x: y=x^4+x \sqrt{x} \cos x-x^2 e^x$

How many different products can be obtained by multiplying two or more of the numbers 3, 5, 7, 11 (without repetition)?

Insert A.M.s between $7$ and $71$ in such a way that the $5^{\text {th }}$ A.M. is $27$ . Find the number of A.M.s.