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Class 10 Maths trigonometry worksheet




Given below are the Class 10 Maths trigonometry worksheet with answers.
a. Match the following
b. True and False
c. Fill in the blanks
d. Short Answer Type
e. Long Answer Type

Match the Following

Question 1.
Match the Following
Class 10 trigonometry worksheet With Solutions

True and False

Question 2.
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 3.
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. $sin^4 A - cos^4 A = sin^2 A - cos^2 A = 2sin^2 A - 1 = 1 - 2 cos^2 A$

Fill in the blanks

Question 4
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. $(1 + tan^2 A ) (1 + sinA ) (1 - sin A) =$ ________.

Short Answer type

Question 5.
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 6.
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 7.
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 8.
If $\sin A =\frac {3}{5}$ .find cos A and tan A.

Question 9.
If $cosec A = \sqrt {10}$. find other five trigonometric ratios.

Question 10.
In a right triangle ABC right angled at B if $sin A =\frac {3}{5}$ . find all the six trigonometric ratios of C.

Question 11.
The value of $(sin30 ^{\circ} + cos30^{\circ}) - (sin60^{\circ} + cos60^{\circ})$ is


Question 12.
If $sin B =\frac {1}{2}$ , show that $3 cos B - 4 cos^3 B = 0$

Question 13.
If $tanA + \frac {1}{tanA}= 2$, find the value of $tan^2 A + \frac {1}{tan^2 A}$

Question 14. Evaluate the following:
$2 sin^2 30^{\circ} - 3cos^2 45^{\circ} + tan^2 60^{\circ}$

Question 15. 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 16. Evaluate:
$cot^2 30^{\circ} - 2 cos^2 60^{\circ} - \frac {3}{4} sec^2 45^{\circ} - 4sec^2 30^{\circ}$

Question 17. Prove that:
$cos 1^{\circ}.cos 2^{\circ} .cos3^{\circ} .... cos 180^{\circ} = 0$

Long Answer Type

Question 18
Prove the following identity
$(sin A - cosec A)^2 + (cos A - sec A)^2 = tan^2 A+cot^2 A-1$
Question 19
Prove the following identity
(i) $cos^6 A + sin^6 A = 1 - 3 sin^2 A Cos^2 A$
(ii)$\frac {1}{cot A + tan A} = sin A cos A$
Question 20
Prove the following
(i) $(sin A + cos A)(cot A + tan A)=sec A + cosec A$
(ii)$sin 30 cos 60 + sin 60 cos 30=1$

Summary

This Class 10 trigonometry worksheet with answers is prepared keeping in mind the latest syllabus of CBSE . This has been designed in a way to improve the academic performance of the students. If you find mistakes , please do provide the feedback on the mail.You can download in PDF form also using the below links


Download Trigonometry worksheet as pdf
link to this page by copying the following text
Also Read




Go back to Class 10 Main Page using below links
Class 10 Maths Class 10 Science

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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