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Valuebased Questions 
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Q1. What is the maximum value of
Hint: ∵ = 3 sin θ
Since the maximum value of ‘sin θ’ is 1
∴ the maximum value of 3 sin θ is 3 × 1 i.e. 3
⇒ the maximum value of is 3.
Q2. If sin θ = 1/3, then find the value of 9 cot^{2}θ + 9.
Hint: cot^{2} θ = cosec^{2} θ – 1
∴ 9 cot^{2}θ + 9 = 9(8) + 9 = 72 + 9 = 81
Q3. If 4 tan θ = 3, then find the value of
Hint:
Q4. If sin α = 1/2 and cos β = 1/2 then find the value of (α + β).
Hint:
Q5. If sin θ + cos θ = √3 , find the value of tan θ + cot θ .
Hint: sin θ + cos θ = √3 ⇒ (sin θ + cos θ)^{2} = 3
⇒ sin^{2} θ + cos^{2} θ + 2 sin θ . cos θ = 3
⇒ 1 + 2 sin θ . cos θ = 3 ⇒ 2 sin θ . cos θ = 2 [∴ sin^{2}θ + cos^{2}θ = 1]
⇒ sin θ . cos θ =1 ⇒ 1 =
⇒
Thus, tanθ + cotθ = 1
Q6. cos (A+B) = 1/2 and sin (A–B) = 1/2 ; 0° < (A + B) < 90° and (A – B) > 0°. What are the values of ∠A and ∠B?
Hint:
...(1)
...(2)
Adding (1) and (2), 2A = 90 ⇒ A = 45
From (1) 45° + B = 60° ⇒ B = 60° – 45° = 15°
Thus, ∠A = 45° and ∠B = 15°
Q1. A group of students plan to put up a banner in favour of respect towards girls and women, against a wall. They placed a ladder against the wall such that its foot is at a distance of 2.5 m from the wall and its top reaches a window 6 m above the ground.
(i) Find the length of the ladder.
(ii) Which mathematical concept is used in this problem?
(iii) By putting up a banner in favour of respect to women, which value is depicted by the group of students?
Sol. (i) Let AB be the ladder and CA be the wall with the window at A. Also,
BC = 2.5 m
CA = 6m
∴ In rt ΔACB, we have
AB^{2} = BC^{2} + CA^{2} [Using Pythagoras Theorem]
= (2.5)^{2} + (6)^{2}
= 6.25 + 36 = 42.25
⇒
Thus, the length of the ladder is 6.5 m.
(ii) Triangles (Pythagoras Theorem)
(iii) Creating positive awareness in public towards regards to women.
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