Using
\[ \cot(A − B) = \frac{\cot A \cot B + 1}{\cot B − \cot A} \]
Find the value of cot 15°
2 + √3
cot 15° = cot(45° − 30°)
Apply identity:
cot(A−B) = (cot A · cot B + 1) / (cot B − cot A)
cot 45° = 1, cot 30° = √3
⇒ (1·√3 + 1)/(√3 − 1) = (√3 + 1)/(√3 − 1)
Multiply numerator and denominator by (√3 + 1):
⇒ (√3 + 1)² / (3 − 1) = (3 + 2√3 + 1)/2 = (4 + 2√3)/2 = 2 + √3
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Important Questions from Trigonometry
If A is an acute angle and tanA + cotA = 2, find the value of 7tan⁸A – 6cot⁸A + 8sec²A.
If p = sinA / (1 + cosA), then sinA / (1 - cosA) is equal to:
In a ΔABC, right-angled at B if tanC = √3, then find (sin²C + cos²C) / (1 + cot²C).
If 8cotθ = 7, then the value of (1 + sinθ) / cosθ) is:
For any acute angle θ, sin²θ + cos²θ = 1. Then the value of cos²θ + cos⁴θ is:
