Home›MPPSC Forest›State Forest Service Mains Exam›Section 'B': Forestry and General Science›UNIT-10: Elementary Mathematics and General Mental Ability›Circular measure, definitions of trigonometric ratio, simple problems on height and distance›If \sin\theta = \frac{1}{2} (where \theta < 90^\circ), then

If sin⁡θ=12\sin\theta = \frac{1}{2}sinθ=21​ (where \t\t\ttheta < 90^\circ)$, then 4cos⁡3\t4\cos^3\t4cos3\ttheta - 3\cos\theta$ is :

20181M#mppsc-forest#pyq#mcq#2018
A.0Correct
B.1
C.12\frac{1}{2}21​
D.None of these
Explanation & Solution

Correct Answer: (A) 0

Given sin⁡\sinsinθ\thetaθ = 12\frac{1}{2}21​ with θ\thetaθ < 90^\circ, we find \theta = 30^\circ. The trigonometric identity \cos(3\theta) = 4\cos^3\theta - 3\cos\theta applies, and since \theta = 30^\circ, 3\theta = 90^\circ, so \cos(90^\circ) = 0.

हिंदी में प्रश्न एवं आदर्श उत्तर

यदि sin⁡θ=12\sin\theta = \frac{1}{2}sinθ=21​ (जहाँ \t\t\ttheta < 90^\circ)$, तब 4cos⁡3\t4\cos^3\t4cos3\ttheta - 3\cos\theta$ है:

A.0सही
B.1
C.12\frac{1}{2}21​
D.इनमें से कोई नहीं

सही उत्तर: (A) 0

दिया गया है sin⁡\sinsinθ\thetaθ = 12\frac{1}{2}21​ (जहाँ θ\thetaθ < 90^\circ), जिससे \theta = 30^\circ प्राप्त होता है। त्रिकोणमितीय सर्वसमिका \cos(3\theta) = 4\cos^3\theta - 3\cos\theta के अनुसार \theta = 30^\circ रखने पर \cos(90^\circ) = 0 प्राप्त होता है।

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