Evaluate the following: ( 0^ + 45^ + 30^ )( 90^ - 45^ + 60^ ) - Vidyadip

Question

Evaluate the following:
$(\cos0^\circ+\sin45^\circ+\sin30^\circ)(\sin90^\circ-\cos45^\circ+\cos60^\circ)$

✓

Answer

$(\cos0^\circ+\sin45^\circ+\sin30^\circ)(\sin90^\circ-\cos45^\circ+\cos60^\circ)\dots(\text{i})$ By trigonometric ration we have $\cos0^\circ=1,\ \sin45^\circ=\frac{1}{\sqrt{2}},\ \sin30=\frac{1}{2},$$\sin90^\circ=1,\cos45^\circ=\frac{1}{\sqrt{2}}\cos60^\circ=\frac{1}{2}$
By substituting above values in (i), we get $\Big(1+\frac{1}{\sqrt{2}}+\frac{1}{2}\Big)\Big(1-\frac{1}{\sqrt{2}}+\frac{1}{2}\Big)$ $\Big[\frac{3}{2}+\frac{1}{\sqrt{2}}\Big]\Big[\frac{3}{2}-\frac{1}{\sqrt{2}}\Big]$ $\Rightarrow\Big[\frac{3}{2}\Big]^2-\Big[\frac{1}{\sqrt{2}}\Big]=\frac{9}{4}-\frac{1}{2}=\frac{7}{4}$

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

Calculate the median for the following distribution:

Marks Obtained	Number of students
Below 10	6
Below 20	15
Below 30	29
Below 40	41
Below 50	60
Below 60	70

Solve the pair of linear equations by substitution method: 0.2x + 0.3y = 1.3; 0.4x + 0.5y = 2.3

Write the number of solution of the following pair of linear equations:

$x + 2y - 8 = 0$

Solve for x and y:
2x + 3y = 0,
3x + 4y = 5

The interior of a building is in the form of a cylinder of base radius 12m and height 3.5m, surmounted by a cone of equal base and slant height 12.5m. Find the internal curved surface area and the capacity of the building.

Prove the following identities:
$\frac{\cos\theta}{(1-\tan\theta)}+\frac{\sin^2\theta}{(\cos\theta-\sin\theta)}=(\cos\theta+\sin\theta)$

In a game, the entry fee is Rs. $5$. The game consists of a tossing a coin $3$ times. If one or two heads show, Sweta gets her entry fee back. If she throws 3 heads, she receives double the entry fees. Otherwise she will lose. For tossing a coin three times, find the probability that she:

loses the entry fee.
gets double entry fee.
just gets her entry fee.

If the ratio of the height of a tower and the length of its shadow is $\sqrt{3}:1,$ what is the angle of elevation of the Sun?

Find the roots of the following equations, if they exist, by applying the quadratic formula:$4\sqrt3\text{x}^2+5\text{x}-2\sqrt3=0$

If the point $P(2,2)$ is equidistant from the points $A(-2, k)$ and $B(-2 k,-3)$, find $k$. Also, find the length of $A P$.