Question
Download Solution PDFIf tan θ + cot θ = 6, then the value of tan2 θ + cot2 θ is ____ .
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
tan θ + cot θ = 6.
Formulas used:
tan θ = 1 / cot θ
(a + b)2 = a2 + b2 + 2ab
Calculation:
tan θ + cot θ = 6
Squaring on both sides,
⇒ (tan θ + cot θ)2 = tan2θ + cot2θ + 2tanθcotθ
⇒ 62 = tan2θ + cot2θ + 2 × 1 / cotθ × cotθ
⇒ 36 = tan2θ + cot2θ + 2
⇒ tan2θ + cot2θ = 34
∴ The correct answer is 34.
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