Consider the following statements: 1.If $\sin A = \sin B$ then we have $\sin \,\,2A = \sin \,\,2B\;$ always 2.The value of ${\rm{\;cos}}\,\,\frac{\pi }{7}\,\,\cos \,\,\frac{{4\,\pi }}{7}\,\,\cos \,\,\frac{{5\,\pi }}{7}{\rm{\;is}}\,\;\frac{1}{4}$ Which of the statements given above is/are correct?

Neither $\left( {\rm{1}} \right)$ nor $\left( {\rm{2}} \right)$

Both $\left( {\rm{1}} \right)$ and $\left( {\rm{2}} \right)$

JEE MATHEMATICS MCQ: TRANSFORMATIONS

1 Easy

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Analyzing +4 | -1

Consider the following statements:

1.If

\sin A = \sin B

then we have

\sin \,\,2A = \sin \,\,2B\;

always

2.The value of

\mathrm{\;cos}\,\,\frac{\pi }{7}\,\,\cos \,\,\frac{{4\,\pi }}{7}\,\,\cos \,\,\frac{{5\,\pi }}{7}\mathrm{\;is}\,\;\frac{1}{4}

Which of the statements given above is/are correct?

View answer and explanation

Correct option: D

Neither

\left( \mathrm{1} \right)

nor

\left( \mathrm{2} \right)

Option D (Neither (1) nor (2)) is correct because statement 1 is not always true, and the value in statement 2 is

\frac{1}{8}

, not

\frac{1}{4}