Complementary Angles — Important Questions
ICSE · Class 9 · Mathematics
41 important questions from Complementary Angles for ICSE Class 9 Mathematics, with answers. Part of the ICSE Class 9 Mathematics syllabus.
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Important Questions from Complementary Angles
Which of the following are equal to tan 40°?
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cot 50°, cot(90° - 40°), sin 40°/cos 40°, cos 50°/sin 50°
tan 40° = cot(90° - 40°) = cot 50°. Also, tan 40° = sin 40°/cos 40°. Since 40° and 50° are complementary, cos 50° = sin 40° and sin 50° = cos 40°, so cos 50°/sin 50° = sin 40°/cos 40° = tan 40°.
Calculate: tan 45° × cot 45°
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1
We know that tan 45° = 1 and cot 45° = 1. Therefore, tan 45° × cot 45° = 1 × 1 = 1. Alternatively, since cot θ = 1/tan θ, we have tan θ × cot θ = 1 for any angle θ (except where undefined).
Which of the following statements are true?
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sin 30° = cos 60°, tan 45° = cot 45°, sec 70° = cosec 20°
For complementary angles: sin 30° = cos(90° - 30°) = cos 60° ✓. tan 45° = cot 45° = 1 ✓. sec 70° = cosec(90° - 70°) = cosec 20° ✓. However, sin 40° ≠ cos 40° since they're equal only when the angle is 45°.
Find the value of: cos 0° + cos 30° + cos 60° + cos 90°
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1 + √3/2 + 1/2 + 0
cos 0° = 1, cos 30° = √3/2, cos 60° = 1/2, cos 90° = 0. Therefore, the sum = 1 + √3/2 + 1/2 + 0 = 3/2 + √3/2 = (3 + √3)/2.
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