Question
Download Solution PDFWhat is the value of x that satisfies 4 cos2 30° + 2x sin 30° - cot2 30° - 6 tan 15° tan 75° = 0 ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula used:
cos(30°) = √3/2
sin(30°) = 1/2
cot(30°) = √3
tan (90° - θ) = cot θ
tan θ × cot θ = 1
Calculation:
4 cos2 30° + 2x sin 30° - cot2 30° - 6 tan 15° tan 75° = 0
Since, tan (90° - θ) = cot θ
⇒ 4 cos2 30° + 2x sin 30° - cot2 30° - 6 tan (90° - 75°) tan 75° = 0
⇒ 4 cos2 30° + 2x sin 30° - cot2 30° - 6 cot 75° tan 75° = 0
But, tan θ × cot θ = 1
⇒ 4 cos2 30° + 2x sin 30° - cot2 30° - 6 = 0
Using the trigonometric values
⇒ 4(√3/2)2 + 2x(1/2) - (√3)2 - 6= 0
⇒ 3 + x - 3 - 6 = 0
∴ x = 6
Last updated on Jun 18, 2025
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