COMPLETE TRIGONOMETRY
In figure, ∆PQR right angled at Q, PQ = 6 cm and PR = 12 cm.
Determine ∠QPR and ∠PRQ. (2013)
3
and 𝐶𝑜𝑠 (𝐴 + 4𝐵)
2
If 𝑆𝑖𝑛 (𝐴 + 2𝐵) =
= 0, 𝐴 > 𝐵 and
𝐴 + 4𝐵 ≤ 90 ° then find A and B. [CBSE 2018]
Find the value of 2 sin6 𝜃 + cos6 𝜃 − 3 sin4 𝜃 + cos4 𝜃 + 1.
CBSE 2020
Prove that sin4 𝜃 − cos4 𝜃 + 1 𝑐𝑜s𝑒𝑐2 𝜃 = 2.
CBSE 2020
tan2 𝐴
cosec2 𝐴
Prove that 2
+ 2
tan 𝐴−1
sec 𝐴−cosec2 𝐴
=
1
.
2
1−2 cos 𝐴
CBSE 2019
0°
Sin θ
Cos θ
Tan θ
30°
45°
60°
90°
A ladder is leaning against a wall of a house such that its upper end is
touching the top of the wall. The foot of the ladder is 2 m away from the wall
and the ladder is making an angle of 60° with the level of the ground. Find the
height of the wall. Also, find the length of the ladder. [CBSE 2017] [3 Marks]
From the top of a 7 m building, the angle of elevation of the top of a cable
tower is 60° and the angle of depression of its foot is 45°. Determine the
height of the tower. (Use √ 3 = 1.73) [CBSE 2020] [4 Marks]
A man standing on the deck of a ship, which is 10 m above water level,
observes the angle of elevation of the top of a hill as 60° and the angle of
depression of the base of hill as 30°. Find the distance of the hill from the ship
and the height of the hill. [CBSE 2016] [3 Marks]
A straight highway leads to the foot of a tower. A man standing at the top of
the tower observes a car at an angle of depression of 30° , which is
approaching the foot of the tower with a uniform speed. After covering a
distance of 50 m, the angle of depression of the car becomes 60°. Find the
height of the tower. ( Use √ 3 = = 1.73) [CBSE 2020] [4 Marks]
As observed from the top of a 100 m high light house from the sea-level , the
angles of depression of two ships are 30° and 45°. If one ship exactly behind
the other on the same side of the light house, find the distance between the
two ships. (Use √ 3 = 1.732) [CBSE 2018] [4 Marks]