NIMCET 2011
The general solution of is
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Answer: Option C — No solution
Detailed Solution
.
Its largest value is , which is less than , so the equation has no solution.
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At the expression reaches its maximum .⚠ Common trap
Options (A), (B) and (D) come from solving mechanically without first checking the range .Quick tip
no solution
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Trigonometric Equations — Preparation
This question tests your understanding of Trigonometric Equations, a key topic in the Quantitative Aptitude section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.
A trigonometric equation is an equation involving trigonometric functions of an unknown angle, such as 2 sin x = 1. This topic covers finding principal solutions (usually between 0 and 2 pi) and general solutions, which include all possible angles. The key general solutions are: sin x = sin a gives x = n pi + (-1)^n a, cos x = cos a gives x = 2n pi +/- a, and tan x = tan a gives x = n pi + a, where n is any integer. Exam questions involve reducing an equation to one of these standard forms, often by factorising or using identities, and then counting the number of solutions in a given interval. Always check that solutions do not make any term in the original equation undefined. Practise the trigonometric equations questions below, each with a step-by-step solution.