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$cos invisible function application left parenthesis alpha minus beta right parenthesis equals 1 text and end text cos invisible function application left parenthesis alpha plus beta right parenthesis equals 1 over c$ where $alpha comma beta element of left square bracket negative pi comma pi right square bracket$ Pairs $alpha comma beta$ which satisfy both the equations is/are

0
1
2
4

The correct answer is: 4

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The number of integral values of k for which the equation $7 cos invisible function application x plus 5 sin invisible function application x equals 2 k plus 1$ has a solution is

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The number of distinct real roots of $open vertical bar table attributes columnalign center center center columnspacing 1em end attributes row cell sin invisible function application x end cell cell cos invisible function application x end cell cell cos invisible function application x end cell row cell cos invisible function application x end cell cell sin invisible function application x end cell cell cos invisible function application x end cell row cell cos invisible function application x end cell cell cos invisible function application x end cell cell sin invisible function application x end cell end table close vertical bar equals 0$ in the interval $negative pi over 4 less or equal than x less or equal than pi over 4$ is

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If $0 less or equal than x less than 2 pi$ , then the number of real values of x, which satisfy the equation $cos invisible function application x plus cos invisible function application 2 x plus cos invisible function application 3 x plus cos invisible function application 4 x equals 0$ is :

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The number of solutions of the equation $cos squared invisible function application open parentheses x plus pi over 6 close parentheses plus cos squared invisible function application x minus 2 cos invisible function application open parentheses x plus pi over 6 close parentheses cos invisible function application open parentheses pi over 6 close parentheses equals sin squared invisible function application pi over 6$ in the interval $left parenthesis negative pi divided by 2 comma pi divided by 2 right parenthesis$ is

The number of solutions of the equation $cos squared invisible function application open parentheses x plus pi over 6 close parentheses plus cos squared invisible function application x minus 2 cos invisible function application open parentheses x plus pi over 6 close parentheses cos invisible function application open parentheses pi over 6 close parentheses equals sin squared invisible function application pi over 6$ in the interval $left parenthesis negative pi divided by 2 comma pi divided by 2 right parenthesis$ is

The possible values of $theta element of left parenthesis 0 comma pi right parenthesis$ such that $sin invisible function application theta plus sin invisible function application 4 theta plus sin invisible function application 7 theta equals 0$ are :

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parallel

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