If 12sin θ = 5 cos θ, then sin θ + cos θ – cot θ is equal to:
Show answer & explanation
Correct answer: B
Explanation
Correct Answer is option 2 i.e. -71/65
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Concept |
Understanding |
Application |
Fair calculation |
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tan θ = P/B sin θ = P/H cos θ = B/H cot θ = B/P Pythagoras theorem: H2 = P2 + B2
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Given 12sin θ = 5 cos θ ⇒ tan θ = 5/12 = P/B |
Hence, H = √(52+122) H = 13 Now, sin θ + cos θ – cot θ = 5/13 + 12/13 – 12/5 = -71/65 |
√(52+122 ) = √(25+144) = √169 = 13 5/13 + 12/13 – 12/5 = (25 + 60 – 156)/65 = -71/65 |