# Trigonometry Important Questions for Class 10 Maths

Question 1.
If $sec X= a + \frac {1}{4a}$, prove that $sec X+ tan X=2a \; or \; \frac {1}{2a}$

Question 2.
If $Sin A+ Sin^2 A= 1$, then find the value of $(cos^2 A+cos^4 A)$.

Question 3
If $x(cos A) - y(sin A) = a$, $x(sin A) + y(cos A) = b$, the tick mark whichever option is correct
a. $x^2 -y^2 = a^2 -b^2$
b. $x^2 +y^2 = a^2 +b^2$
c. $x^2 +y^2 = a^2 - b^2$
d. $x^2 -y^2 = a^2 + b^2$

Question 4
If $tan 2A = cot (A - 18^{\circ})$, where 2A is an acute angle. Find the value of A.

Question 5
If $tan (A+B) = \sqrt {3}$ and $tan (A - B) = \frac {1}{\sqrt {3}}$ Find the value of A and B.

Question 6
If $sin (A+B) = 1$ and $cos (A-B) = \frac {\sqrt {3}}{2}$, $0 \leq (A+B) \leq 90 \; ,\; A \geq B$, then find the value of A and B.

Question 7
If $sin \theta - cos \theta = 0$, then Find the value of $(sin^4 \theta + cos^4 \theta)$

Question 8
If $cos A=\frac {1}{2}$, $sin B =\frac {1}{2}$ then value of A +B
a. 30°
b. 60°
c. 90°
d. 120°

Question 9
If $sin (X + Y) = cos (X - Y) =1$ then
a. X = Y = 90°
b. X = Y = 0°
c. X = Y = 45°
d. X = 2Y

Question 10
If $sec \theta + tan \theta =p$ then find the value of $cosec \theta$

Question 11
If A and B acute angles such that $tan A = \frac {1}{2}$ , $tan B = \frac {1}{3}$ and
$tan (A + B) =\frac { tan A + tan B}{1- tan A tan B}$, find A + B.

Question 12
Prove that
a. $tan 10^{\circ} tan 15^{\circ} tan 75^{\circ} tan 80^{\circ} = 1$
b. $tan 1^{\circ} tan 2^{\circ} tan 3^{\circ} .... tan 89^{\circ} = 1$
c. $cos 1^{\circ} cos 2^{\circ} cos3^{\circ} .... cos 180^{\circ} = 0$

Question 13
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

a. $\frac {cos A}{1 + sin A} + \frac {1 + sin A}{cos A} = 2 sec A$
b. $\frac {1 + sec A}{sec A} = \frac {sin^2 A}{1- cos A}$
c. $\sqrt { \frac {1+ sin A}{1- sin A} } = sec A + tan A$

Question 14
In a $\Delta ABC$ right angled at C, if $tan A = \frac {1}{\sqrt {3}}$ find the value of
$sin A cos B + cos A sin B$.

Question 15

If $sec \theta - tan \theta = x$, show that:
$sec \theta = \frac {1}{2} [x + \frac {1}{x}]$
$tan \theta =\frac {1}{2} [\frac {1}{x} -x]$

Question 16.
If $tan \theta = \frac {12}{5}$
Find the value $\frac {1+ sin \theta }{1 -sin \theta }$

Question 17
If $sin \theta + cos \theta = \sqrt {2} cos (90 - \theta)$,find $cot \theta$

Question 18
Prove that
If $tan^2 \theta = 1 -p^2$, then prove that $sec \theta + tan^3 \theta cosec \theta = (2 - p^2) ^ {3/2}$.

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### 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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