{sin ^2}{5^o} + {sin ^2}{10^o} + {sin ^2}{15^ | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(d) Given expression is

${\sin ^2}{5^o} + {\sin ^2}{10^o} + {\sin ^2}{15^o} + ..... + {\sin ^2}{85^o} + {\sin ^2}{90^o}.$

We know that $\sin {90

Vedclass · Accepted Answer

$9\frac{1}{2}$

Vedclass · Answer

(d) Given expression is

${\sin ^2}{5^o} + {\sin ^2}{10^o} + {\sin ^2}{15^o} + ..... + {\sin ^2}{85^o} + {\sin ^2}{90^o}.$

We know that $\sin {90^o} = 1$ or ${\sin ^2}{90^o} = 1$.

Similarly, $\sin {45^o} = \frac{1}{{\sqrt 2 }}{m{or}}\,{m{si}}{{m{n}}^{m{2}}}{45^o} = \frac{1}{2}$

and the angles are in $A.P. $ of $18$ terms.

We also know that ${\sin ^2}{85^o} = {[\sin ({90^o} - {5^o})]^2}$$ = {\cos ^2}{5^o}.$

Therefore from the complementary rule, we find

$	herefore$ ${\sin ^2}{5^o} + {\sin ^2}{85^o} = {\sin ^2}{5^o} + {\cos ^2}{5^o} = 1.$

Therefore,

${\sin ^2}{5^o} + {\sin ^2}{10^o} + {\sin ^2}{15^o} + ... + {\sin ^2}{85^o} + {\sin ^2}{90^o}$

$ = (1 + 1 + 1 + 1 + 1 + 1 + 1 + 1) + 1 + \frac{1}{2} = 9\frac{1}{2}$.

${\sin ^2}{5^o} + {\sin ^2}{10^o} + {\sin ^2}{15^o} + ... + $ ${\sin ^2}{85^o} + {\sin ^2}{90^o} = . ..$

Similar Questions

$\cot x - \tan x = $

$2 \sin \left(12^{\circ}\right)-\sin \left(72^{\circ}\right)$ નું મુલ્ય ............ છે.

ચાપની લંબાઈ $15cm$ હોય અને તેને કેન્દ્ર આગળ આંતરેલો ખૂણો $3/4$ રેડિયન હોય વર્તુળની ત્રિજ્યા.......$cm$ માં મેળવો ?

$\cos A - \sin A$ જયારે $A = \frac{{5\pi }}{4}, = . . . . $

જો સમીકરણ ${\sin ^2}\theta = \frac{{{x^2} + {y^2}}}{{2xy}},x,y, \ne 0$ શકય હોય તો