Q1: sin^{2} 60° + 2 tan 45°  cos^{2} 30° [Allahabad 2019]
Ans: 2
Q2: If sin x + cos y = 1; x = 30° and is an acute angle, find the value of y. [CBSE 2019 (30/5/1)]
Ans: We have, sin x + cosy = 1
⇒ sin30° + cosy = 1
⇒ y = 60^{0}
Q3: Prove that: (1 + cot A  cosec A)(l + tan A + sec A) = 2 [CBSE 2019 (30/1/2)]
Ans: LHS = (1 + cotAcosecA) (1 + tanA +secA)
Q4: Prove that: [CBSE 2019 (30/5/1)]
Ans:
Q 5: If cos θ + sin θ = √2cos θ , show that cos θ  sin θ = √2 sin θ. [CBSE 2019 (30/ 5/ 1)]
Ans: Given: cos θ + sin θ = √2cos θ
Now, (cos θ + sin θ)^{2} + ( cos θ  sin θ)^{2}
cos^{2}θ + sin^{2}θ + 2cosθ. sin θ + cos^{2}θ + sin^{2}θ  2cosθ. sinθ
1 + 1 = 2
Again, (cos θ + sin θ)^{2} + (cos θ  sin θ)^{2} = 2
⇒ (√2 cosθ)^{2} + (cos θ  sin θ)^{2} = 2
⇒ 2 cos^{2}θ + ( cos θ  sin θ)^{2} = 2
⇒ (cos θ  sin θ)^{2} = 2  2cos^{2}θ = 2 ( 1  cos^{2}θ)
= 2sin^{2}θ
∴ cos θ  sin θ = √2 sin θ
Hence proved
Q6: Prove that: ( sin A + cosec A)^{2} + ( cos A + sec A)^{2} = 7 + tan^{2} A + cot^{2} 4
[CBSE 2019 (30/1/2;]
Ans: LHS = (sin A + cosec A)^{2} + (cos A + sec A)^{2}
=sin^{2} A + cosec^{2} A + 2sinA . cosec A + cos^{2} A + sec^{2} A + 2 cos A .sec A
= (sin^{2} A + cosec^{2} A + 2) + (cos^{2} A + sec^{2} A + 2) (sin A.cosec A = 1)
= (sin^{2} A + cos^{2}A) + (cosec^{2} A + sec^{2} A) + 4 (cos A. sec A = 1)
= 1 + 1+ cot^{2} A + 1 + tan^{2} A + 4
= 7 + tan^{2} A + cot^{2} A = RHS (∵ 1 + cot^{2} A = cosec^{2} A and 1 + tan^{2} A = sec^{2} A)
Q7: If sin (A + 2B) and cos (A + 4B) = 0, A > B, and A + 4B ≤ 90^{0} then find A and B. [CBSE 2018 (C)]
Ans:
So, sin(A + 2B) = sin 60°
Hence A + 2B = 60° ..(i)
Also, we have
cos(A + 4B) = 0
cos(A + 4B) = cos 90°
A + 4B = 90° ..(ii)
Subtracting (ii) from (i), we have
2B =  30°
=> B = 15°
Put B = 15° in eq. (i), we have
A + 2(15°) = 60°
⇒ A + 30° = 60°
⇒ A = 30°
Q1: Prove that: [CBSE 2019 (30/5/1)]
Ans: LHS
Q2: Prove that: [CBSE 2019 (30/5/1)]
Ans: LHS
115 videos478 docs129 tests

1. What is trigonometry and why is it important? 
2. What are the basic trigonometric ratios and how are they used? 
3. How do we find the values of trigonometric ratios for different angles? 
4. How is trigonometry used in realworld applications? 
5. How can trigonometry help in solving problems involving heights and distances? 
115 videos478 docs129 tests


Explore Courses for Class 10 exam
