 # Class 10 Maths trigonometry worksheet

Question 1.
Write the values cos 0°, cos 45°, cos 60° and cos 90°. What happens to the values of cos as angle increases from 0° to 90°?

Question 2.
Write the values of sin 0°, sin 30°, sin 45°, sin 60° and sin 90°. What happens to the values of sin as angle increases from 0° to 90°?

Question 3.
Write the values of tan 0°,tan 30°, tan 45°, tan 60° and tan 90°. What happens to the values of tan as angle increases from 0° to 90°?

Question 4.
If $\sin A =\frac {3}{5}$ .find cos A and tan A.

Question 5.
If $cosec A = \sqrt {10}$. find other five trigonometric ratios.

Question 6.
In a right triangle ABC right angled at B if $sin A =\frac {3}{5}$ . find all the six trigonometric ratios of C.

Question 7.
The value of $(sin30 ^{\circ} + cos30^{\circ}) - (sin60^{\circ} + cos60^{\circ})$ is

Question 8.
True and False statement
a. The value of $sin \theta + cos \theta$ is always greater than 1
b. $tan \theta$ increases faster than $sin \theta$ as θ increase
c. The value of the expression $(cos^2 23^{\circ} - sin^2 67^{\circ})$ is positive.
d. The value of the expression $(sin 80^{\circ} - cos80^{\circ})$ is negative.
e. If $cosA + cos^2 A = 1$, then $sin^2 A + sin^4 A = 1$.
f. $(tan \theta + 2) (2 tan \theta + 1) = 5 tan \theta + sec ^2 \theta$.
g. If the length of the shadow of a tower is increasing, then the angle of elevation of the sun is also increasing.
h. If a man standing on a platform 3 metres above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection.
i. If the height of a tower and the distance of the point of observation from its foot, both, are increased by 10%, then the angle of elevation of its top remains unchanged
j. $cos^4 A - cos^2 A = sin^4 A - sin^2 A$
k. $cot^4 A - 1 = cosec^4 A - 2cosec^2 A$
l. $sin^4 A + cos^4 A = 1 - 2 sin^2 A cos^2 A$
m. $sin^4 A - cos^4 A = sin^2 A - cos^2 A = 2sin^2 A - 1 = 1 - 2 cos^2 A$

Question 9.
If $sin B =\frac {1}{2}$ , show that $3 cos B - 4 cos^3 B = 0$

Question 10.
If $tanA + \frac {1}{tanA}= 2$, find the value of $tan^2 A + \frac {1}{tan^2 A}$

Question 11. Evaluate the following:
$2 sin^2 30^{\circ} - 3cos^2 45^{\circ} + tan^2 60^{\circ}$

Question 12. Evaluate:
$sin^2 30^{\circ} cos^2 45^{\circ} + 4tan^2 30^{\circ} + \frac {1}{2} sin^2 90^{\circ} - 2 cos^2 90^{\circ} + \frac {1}{24}cos^2 0^{\circ}$

Question 13. Evaluate:
$cot^2 30^{\circ} - 2 cos^2 60^{\circ} - \frac {3}{4} sec^2 45^{\circ} - 4sec^2 30^{\circ}$

Question 14. Prove that:
$cos 1^{\circ}.cos 2^{\circ} .cos3^{\circ} .... cos 180^{\circ} = 0$

Question 15.
Match the Following Question 16.
True and False
a. $cos A =\frac {4}{3}$ for some angle A.
b. $tan A = \frac {sin A}{cos A}$
c. $secA =\frac {1}{cosA}$ , for an acute angle
d. $sin 60^{\circ} = 2 sin 30^{\circ}$
e. $Sin A + Cos A =1$
f. $1 + cot^2 A =cosec^2 A$
g. $sin A \times cot A= cos A$
h. $cosec 50^{\circ} = sec 40^{\circ}$

Question 17
Fill in the blanks:
a. $5 cos 0^{\circ} + sin 90^{\circ}$ = __________
b. $tan 0^{\circ} =$ _____________
c. $tan 90^{\circ}$ is _____________
d. If $sin A= 1$, then A = ________________
e. $2 sin^2 60^{\circ}$ = ___________
f. $2 cos^2 45^{\circ}$ = __________________
g. $sin^2 A + cos^2 A=$ _______________
h. $(1 + tan^2 A ) (1 + sinA ) (1 - sin A) =$ ________.

Question 18
Prove the following identity
$(sin A - cosec A)^2 + (cos A - sec A)^2 = tan^2 A+cot^2 A-1$

Reference Books for class 10

Given below are the links of some of the reference books for class 10 math.

You can use above books for extra knowledge and practicing different questions.

### Practice Question

Question 1 What is $1 - \sqrt {3}$ ?
A) Non terminating repeating
B) Non terminating non repeating
C) Terminating
D) None of the above
Question 2 The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is?
A) 19.4 cm3
B) 12 cm3
C) 78.6 cm3
D) 58.2 cm3
Question 3 The sum of the first three terms of an AP is 33. If the product of the first and the third term exceeds the second term by 29, the AP is ?
A) 2 ,21,11
B) 1,10,19
C) -1 ,8,17
D) 2 ,11,20

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