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Maths-

General

Easy

Question

The solution(s) of the equation cos2x sin6x = cos3x sin5x in the interval [0, $straight pi$ ] is/are –

$\frac{π}{6}$
$\frac{π}{2}$
$\frac{2 π}{3}$
$\frac{5 π}{6}$

hint Hint:

In this question, we have to find the solution(s) of the equation cos2x sin6x = cos3x sin5x in the interval [0, $straight pi$ ]. Firstly, we will solve the equation to get the possible value of trigonometric terms, later using that value we will find the possible value of x.

The correct answer is: $pi over 6$

$space space space space sin space 5 x. space cos space 3 x space equals sin space 6 x. space cos space 2 x rightwards double arrow 1 half open parentheses sin space 8 x plus sin space 2 x close parentheses equals 1 half open parentheses sin space 8 x plus sin space 4 x close parentheses rightwards double arrow sin space 2 x space minus sin space 4 x space equals 0 rightwards double arrow sin left parenthesis 3 x minus x right parenthesis minus sin left parenthesis 3 x plus x right parenthesis equals 0 rightwards double arrow negative 2 space sin space x. space cos space 3 x space equals 0 rightwards double arrow sin space x equals 0 space o r space cos space 3 x space equals 0 i. e. space x space equals n straight pi left parenthesis straight n element of straight I right parenthesis comma space or space 3 straight x equals 2 kπ plus-or-minus straight pi over 2 left parenthesis straight k element of straight k right parenthesis So comma space straight x element of left square bracket 0 comma space straight pi right parenthesis space then space given space equation space is space satisfied space of space straight x equals 0 comma space straight pi comma space straight pi over 6 comma space straight pi over 2 comma space fraction numerator 5 straight pi over denominator 6 end fraction.$

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