Question
Download Solution PDFIf A is an acute angle, and tan2A + secA = 11, then find the value of cotA.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
tan2A + secA = 11
Formula used:
sec2A = 1 + tan2A
tan2A = sec2A - 1
Calculation:
Let, secA = x
sec2A - 1+ secA = 11
x2 + x - 12 = 0
⇒ (x + 4)(x - 3) = 0
⇒ x = 3 (Since secA must be positive)
Now, secA = 3,
Using cotA = 1/tanA, and tanA = √(sec2A - 1)
⇒ tanA = √(32 - 1) = √8 = 2√2
⇒ cotA = 1/tanA = 1 / (2√2)
∴ The value of cotA is 1 / (2√2).
Last updated on Jul 18, 2025
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