Question
Download Solution PDFIf θ is an acute angle and tanθ + cotθ = 2, then the value of tan2θ + cot2θ + 2 tan5θcot4 θ is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
tanθ + cotθ = 2
Formula Used:
Tan45° = 1
Cot45° = 1
Calculation:
According to the question,
tanθ + cotθ = 2
If we put θ = 45° in the above trigonometric equation, we get
⇒ tan45° + cot45° = 1 + 1 = 2
So,
tan2θ + cot2θ + 2 tan5θcot4 θ = 12 + 12 + 2 × 15 × 14
⇒ 1 + 1 + 2
⇒ 4
∴ The required answer is 4.
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