Qus : 2 Phrases PYQ 2020 1 Angle of elevation of the top of the tower from 3
points (collinear) A, B and C on a road leading to the
foot of the tower are 30°, 45° and 60°, respectively.
The ratio of AB and BC is
1 √ ( 3 ) : 1 2 √ ( 3 ) : 2 3 1 : √ ( 3 ) 4 2 : √ ( 3 ) Go to Discussion Phrases Previous Year PYQ Phrases NIMCET 2020 PYQ Solution According to the given information, the figure should be as follows.
Let the height of tower = h
Qus : 6 Phrases PYQ 2019 2 If A > 0, B > 0 and A + B = π 6 , then the minimum value of t a n A + t a n B
1 2 √ 3 − 2 √ 3
3 2 √ 3
4 √ 2 − √ 3
Go to Discussion Phrases Previous Year PYQ Phrases NIMCET 2019 PYQ Solution On differentiating x= tanA + tan(π/6-A)
we get :
dx/dA = sec²A-sec²(π/6-A)
now putting
dx/dA=0
we get
cos²(A) = cos²(π/6-A) so 0≤A≤π/6
therefore
A=π/6-A from here we get A = π/12 = B
so minimum value of that function is
2tanπ/12 which is equal to 2(2-√3)
Qus : 10 Phrases PYQ 2024 4 The value of tan ( π 4 + θ ) tan ( 3 π 4 + θ ) is
1 -2 2 2 3 1 4 -1 Go to Discussion Phrases Previous Year PYQ Phrases NIMCET 2024 PYQ Solution
We are given:
Evaluate tan ( π 4 + θ ) ⋅ tan ( 3 π 4 + θ )
✳ Step 1: Use identity
tan ( A + B ) = tan A + tan B 1 − tan A tan B
But we don’t need expansion — use known angle values:
tan ( π 4 + θ ) = 1 + tan θ 1 − tan θ
tan ( 3 π 4 + θ ) = − 1 + tan θ 1 + tan θ
✳ Step 2: Multiply
( 1 + tan θ 1 − tan θ ) ⋅ ( − 1 + tan θ 1 + tan θ )
Simplify:
= ( 1 + tan θ ) ( − 1 + tan θ ) ( 1 − tan θ ) ( 1 + tan θ ) = ( tan 2 θ − 1 ) 1 − tan 2 θ = − 1
✅ Final Answer:
− 1
Qus : 11 Phrases PYQ 2024 4 If sin x = sin y and cos x = cos y , then the value of x-y is
1 π / 4 2 n π / 2 3 n π 4 2 n π Go to Discussion Phrases Previous Year PYQ Phrases NIMCET 2024 PYQ Solution
Given:
sin x = sin y and cos x = cos y
✳ Step 1: Use the identity for sine
sin x = sin y ⇒ x = y + 2 n π or x = π − y + 2 n π
✳ Step 2: Use the identity for cosine
cos x = cos y ⇒ x = y + 2 m π or x = − y + 2 m π
? Combine both conditions
For both sin x = sin y and cos x = cos y to be true, the only consistent solution is:
x = y + 2 n π ⇒ x − y = 2 n π
✅ Final Answer:
x − y = 2 n π for n ∈ Z
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