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Class 10 trigonometry Problems with Solutions




Question 1.
Given
$a cosec A = p$ and $b cot A = q$,
then prove that
$\frac {p^2}{a^2} - \frac {q^2}{b^2} =1$


Question 2.
Prove the following trigonometric identities:
a.$cos^2 \theta (1 + tan^2 \theta) = 1$
b. $cos^2 \theta + \frac {1}{1+ cot^2 \theta} =1$
c. $ \frac {1}{1+ sin \theta } + \frac {1}{1-sin \theta } = 2 sec^2 \theta$
d. $cosec^2 \theta + sec^2 \theta =cosec^2 \theta sec^2 \theta$
e.$tan \theta - cot \theta = \frac {2sin^2 \theta -1}{sin \theta cos \theta}$

Question 3.
If A, B, C are interior angles of $\Delta ABC$, show that
$cosec ^2 (\frac {B+C}{2} ) - tan ^2 \frac {A}{2} =1$

Question 4.
If $x = a sec \theta + b tan \theta $ and $y=a tan \theta + b sec \theta $ ,prove that
$x^2 -y^2 = a^2 -b^2$


Question 5
Prove the following identities:
i. $2(sin^6 \theta + cos^6 \theta ) -3 (sin^4 \theta + cos^4 \theta ) + 1=0$
ii. $sin^6 \theta + cos^6 \theta + 2 sin^2 \theta cos ^2 theta =1$
iii. $(sin^8 \theta -cos^8 \theta = (sin^2 \theta -cos^2 \theta) (1 -2sin^2 \theta cos^2 \theta )$




Question 6.
If $cosec A -cot A = q$, then show that
$ \frac {q^2 -1}{q^2 + 1} + cos A =0$


Question 7.
If $x = p sec \alpha cos \beta$, $y = q sec \alpha sin \beta$ and $z = r tan \alpha$, then show that
$\frac {x^2}{p^2} + \frac {y^2}{q^2} -\frac {z^2}{r^2} =1$


Question 8.
Prove that
$ (1+ cot \theta) (1 + tan \theta + sec \theta )=2$

Question 9.
Prove that
cot4 A – 1 = cosec4 A – 2cosec2 A
Question 10.
$ \frac {sin A -cos A +1}{sin A + cos A -1} = \frac {1}{sec A -tan A}$
Question 11.
if $tan A + sin A =m$ and $tan A -sin A =n$
Prove that


Question 12
$ sin A(1 + tan A) + cos A(1 + cot A) = sec A + cosec A$


Question 13
$ \frac {tan A}{1- cot A} + \frac {cot A}{1-tan A} = 1 + tan A + cot A$
Question 14
$\sqrt {sec^2 A + cosec^2 A} = (tan A + cot A)$


Question 15
if $xsin^3 A + ycos^3 A = sin A cos A$
and $x sin A = y cos A$
Prove that
$x^2 + y^2 =1$

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Also Read



Reference Books for class 10

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

  1. Oswaal CBSE Question Bank Class 10 Hindi B, English Communication Science, Social Science & Maths (Set of 5 Books)
  2. Mathematics for Class 10 by R D Sharma
  3. Pearson IIT Foundation Maths Class 10
  4. Secondary School Mathematics for Class 10
  5. Xam Idea Complete Course Mathematics Class 10

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


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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