Trigonometry
- If q be an acute angle and 7 sin²θ + 3 cos²θ = 4, then the value of tan θ is
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7 sin²θ + 3cos²θ = 4
⇒ 7 sin²θ + 3 = 4 = 4 sec²θ cos²θ cos²θ
⇒ 7 tan²θ + 3 = 4(1+ tan²θ)
⇒ 7 tan²θ – 4 tan²θ = 4 – 3
⇒ 3 tan²θ = 1⇒ tan²θ = 1 3 ⇒ tan θ = 1 √3
Correct Option: B
7 sin²θ + 3cos²θ = 4
⇒ 7 sin²θ + 3 = 4 = 4 sec²θ cos²θ cos²θ
⇒ 7 tan²θ + 3 = 4(1+ tan²θ)
⇒ 7 tan²θ – 4 tan²θ = 4 – 3
⇒ 3 tan²θ = 1⇒ tan²θ = 1 3 ⇒ tan θ = 1 √3
- The value of cot 10° . cot 20° . cot 60° . cot 70° . cot 80° is
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cot10°.cot 80°. cot20°. cot70°. cot 60° = cot10°.tan10° . cot 20°. tan 20°. cot 60°
= 1 × 1 × 1 √3 
= 1 √3
Correct Option: D
cot10°.cot 80°. cot20°. cot70°. cot 60° = cot10°.tan10° . cot 20°. tan 20°. cot 60°
= 1 × 1 × 1 √3 = 1 √3
- The angles of a triangle are (x + 5)°, (2x – 3)° and (3x + 4)°. The value of x is
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Sum of angles of a triangle = 180°
∴ x + 5 + 2x – 3 + 3x + 4 = 180°
⇒ 6x + 6 = 180°
⇒ 6x = 180 – 6 = 174°⇒ x = 174 = 29 6
Correct Option: C
Sum of angles of a triangle = 180°
∴ x + 5 + 2x – 3 + 3x + 4 = 180°
⇒ 6x + 6 = 180°
⇒ 6x = 180 – 6 = 174°⇒ x = 174 = 29 6
- The measure of the angles of a triangle are in the ratio 2 : 7 : 11. Measures of angles are
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Let the measure of three angles of triangle are 2x, 7x and 11x respectively.
∴ 2x + 7x + 11x = 180º
⇒ 20x = 180⇒ x = 180 20
∴ First angle = 2x = 2 × 9 = 18°
Second angle = 7x = 7 × 9 = 63°
Third angle = 11x =11 × 9 = 99°Correct Option: B
Let the measure of three angles of triangle are 2x, 7x and 11x respectively.
∴ 2x + 7x + 11x = 180º
⇒ 20x = 180⇒ x = 180 20
∴ First angle = 2x = 2 × 9 = 18°
Second angle = 7x = 7 × 9 = 63°
Third angle = 11x =11 × 9 = 99°
- The value of tan1°tan2° tan3°....... tan89° is :
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tan1°.tan2°.tan3°... tan45°... tan88°tan89°
= (tan1°.tan89°) (tan2°. tan88°) ... tan45°
= (tan1°.cot1°).(tan2°.cot2°) ... tan45° = 1
[∵ tan (90° – θ) = cotθ, tanθ.cotθ = 1]Correct Option: A
tan1°.tan2°.tan3°... tan45°... tan88°tan89°
= (tan1°.tan89°) (tan2°. tan88°) ... tan45°
= (tan1°.cot1°).(tan2°.cot2°) ... tan45° = 1
[∵ tan (90° – θ) = cotθ, tanθ.cotθ = 1]
