Introduction to Trigonometry Class 10 Maths Important Questions
Q 1 – Given that sin α = 1/2 , and cos β = 1/2 , then the value of
(α +β)
(a) 0°
(b) 30°
(c) 60°
(d) 90°
Q 2 – If ABC is right angled triangle at C, then the value of cos (A+B)
(a) 0
(b) 1/√3
(c)√3/2
(d) 1
Q 3 – In ABC, C= 90, the value of 1 +tan2A
(a) sec2 C
(b) cosec2 B
(c) sec2 B
(d) cosec2 C
Q 4 – 2 tan 30º/1 + tan2 30 ºis equal to
a) sin 60°
(b) cot 30°
(c) tan 60°
(d) 2 /tan 30º
Q 5 – 4 tan2α – 4sec2α
(a) – 4
(b) 4
(c) 2
(d) – 2
Q 6 – If x = 3sin β and y =4 cos β, find the value of 
(a) 12
(b) 15
(c) 20
(d) 5
Q 7 – If 2 cos, find the value of 
(a) 2+√3
(b) 2 – √3
(c) √3
(d) None of these
Q 9 – If sec θ+ tan θ = p, show that
Q 10 – If x = a sin α and y = b tan α , then show that 
Q 11 – What happens to the value of tanθ when θ increases from 0° to 90°?
Q 12 – Evaluate: a) sin2 31° + cos2 59° b) sin2 19° + sin2 71°
Q 13 – In ∆ABC right angled at B, AB = 24 cm, BC = 7 cm. Determine
(i) sin A, cos A
(ii) sin C, cos C
Q 14 – In the given figure find tan P – cot R
Q 15 – If sin A = 3/4 calculate cos A and tan A.
Q 16 – Given 15 cot A = 8. Find sin A and sec A.
Q 17 – Given sec θ = 13/12 calculate all other trigonometric ratios.
Q 18 – Find the value of x, if
Q 19 – If ABC is right angled at C, then the value of cos (A + B) is
Q 20 – Prove that: (1 + tan A – sec A) (1 + tan A + sec A) = 2 tan A
Q 21 – If ABC is right angled at C , then find the value of sec (A + B)
Q 22 – Assertion The value of sin θ = 4/3 is not possible.
Reason Hypotenuse is the largest side in any right angled triangle.
(a) Both assertion (A) and reason (R) are true and reason
(R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason
(R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Q 23 – Assertion : sin2 67 + cos2 67 = 1
Reason : For any value of θ sin2 θ + cos2 θ = 1
(a) Both assertion (A) and reason (R) are true and reason
(R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason
(R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Q 24 – If cos (α + β) = , then find sin (α -β) in terms of β.
Q 25 – The value of the tan2 60º + sin2 45 º) is……….
Q 26 – In the adjoining figure, what is the length of BC ?
Q 27 – If sec θ sin θ = 0, then find the value of θ.
Q 28 – What happens to value of cos θ when θ increases from 0º to 90º
Q 29 – Find the value of sin2 41 + sin2 49
Q 30 – Evaluate: 
Q 31 – In the given figure, AOB is a diameter of a circle with centre O, find tan A tan B.
Q 32 – Express the trigonometric ratio of sec A and tan A in terms of sin A.
Q 33 – Find the value of tan2 10 – cot2 80.
Q 34 – If A and B are acute angles and sin A= cos B, then find the value of A + B
Q 35 – Find the value of cot 10º cot 30º cot 80