Evaluate the following: 45^ 30^ + 45^ 30^ - Vidyadip

Question

Evaluate the following:
$\sin 45^{\circ} \sin30^{\circ} +\cos 45^{\circ} \cos30^{\circ}$

✓

Answer

$\sin 45^{\circ} \sin30^{\circ} +\cos 45^{\circ} \cos30^{\circ}\ \dots(1)$ We know that by trigonometric ratios we have, $\sin45^\circ =\frac{1}{\sqrt2}\ \sin30^\circ=\frac{1}{\sqrt2}$ $\cos45^\circ=\frac{1}{\sqrt2}\ \cos30^\circ=\frac{\sqrt3}{2}$ Substituting the values in (i) we get $\frac{1}{\sqrt2}.\frac{1}{2}+\frac{1}{\sqrt2}.\frac{\sqrt3}{2}$$=\frac{1}{\sqrt2}.\frac{\sqrt3}{2\sqrt2}=\frac{\sqrt3+1}{2\sqrt2}$

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 "3 Marks Question" from Trigonometric Ratios→Trigonometric Ratios — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

The common tangents AB and CD to two circles with centres O and O’ intersect at E between their centres. Prove that the points O, E and O’ are collinear.

A T.V. Tower stands vertically on a bank of a river. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From a point 20m away this point on the same bank, the angle of elevation of the top of the tower is 30°. Find the height of the tower and the width of the river.

Find the sum of the following arithmetic progressions:
$1, 3, 5, 7, .....$ to $12$ terms.

$\sqrt{\frac{\sec \theta-1}{\sec \theta+1}}+\sqrt{\frac{\text { sec } \theta+1}{\sec \theta-1}}=2 \operatorname{cosec} \theta$

The length of the diagonal of a square is 24cm. Find its area.

Prove that a diameter AB of a circle bisects all those chords which are parallel to the tangent at the point A.

Prove that:
$\cot\theta\tan(90^\circ-\theta)-\sec(90^\circ-\theta)\text{cosec }\theta\\+\sqrt{3}\tan12^\circ\tan60^\circ\tan78^\circ=2$

The mean of the following frequency distribution is $25$. Find the value of $f.$

Class:	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
Frequency:	$5$	$18$	$15$	$f$	$6$

The following table gives the ages of 1000 persons who visited a shopping centre on Sunday:

Age (in years)	0-10	10-20	20-30	30-40	40-50	50-60	60-70
Number of persons	105	222	220	138	102	113	100

Find the mean number of the people who visited a shopping centre on Sunday

Solve for $x, \frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30}, x \neq-4,7$.