Question
Statement-I : If and
then
Statement-II : If sinA = sinB and cosA = cosB, then
- Statement-I is True, Statement-II is True; Statement-II is a correct explanation for Statement-I.
- Statement-I is True, Statement-II is True; Statement-II is NOT a correct explanation for Statement-I
- Statement-I is True, Statement-II is False
- Statement-I is False, Statement-II is True
Hint:
In this question, given two statements. It is like assertion and reason. Statement1 is assertion and statement 2 is reason, Find the statement 1 is correct or not and the statement 2 correct or not if correct then is its correct explanation.
The correct answer is: Statement-I is True, Statement-II is False
Here, we have to find the which statement is correct and if its correct explanation or not.
Firstly,
Statement-I:
and
then ![straight A equals straight n pi plus straight B comma space straight n element of straight I](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHUAAAAPCAYAAADavYAbAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAf5JREFUeNpjYMAOKhlGwX8ofgzEN4B4HRBLD3L34gQGUAUao5GKAiKB+CQd7QeF/wQgPgfE34D4F4GIwxupi4F4LhQP94giRS0TNGDpAYKA+AoQZwCxMRCzUeI3WWhRAwLXoHxaBm4oEN8F4h9AfBCPfVnQ1PofDy6ncaTKQnMNLf2JbA8XtRJsDzQAYQHZRWS9gw/j0hcKNV8eKpYI9TA2sBDq2TVAHIAkDuL70DingnKoG9RtxmQENCn+BIFJaH6kyG880NQEy+osQHwfKk6LnOpIRvF2Fy2Vg9wnTsNIheGXQKxDJ38+haqhSqSCWry1aGK1RBZr1Krb8AU6C7QIRuZ/oVFJguwWUCJ3AeItQKxHB3/+otC9KAEEygWCaOIg/i08KYeS4pdUz1oC8X40/l46NpQ00OynVaRSLadmEIiY5EGQU0FdivlI/HBoXUuvSGWANnRo7c8J1KpTQc1nJRyK5aHyAx2p06CNDBhoBuIpdO7SfKGDP0FthjNktGVQzPSCtiLxgeVQdQMZqXehAyMw0ArEu4FYhYTmP7mRCkrY1Wglw3KomgAq+xNWCsH6qQbQ6pEkv4Ga16YENICa8ocHMFIDsPQRQW7+BB0soVVfGoZ/QO0RpFOkYhtR+kPJiNIoIB5QuwQbBQMMDKBFJMtoUAwfIE3iwAfdAAA3ms6KhiAj8wAAASh0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+QTwvbWk+PG1vPj08L21vPjxtaSBtYXRodmFyaWFudD0ibm9ybWFsIj5uPC9taT48bWk+JiN4M0MwOzwvbWk+PG1vPis8L21vPjxtaSBtYXRodmFyaWFudD0ibm9ybWFsIj5CPC9taT48bW8+LDwvbW8+PG1vPiYjeEEwOzwvbW8+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPm48L21pPjxtbz4mI3gyMjA4OzwvbW8+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPkk8L21pPjwvbWF0aD7WBqVkAAAAAElFTkSuQmCC)
......(i)
![rightwards double arrow 1 minus s i n squared A equals 1 minus s i n squared B](data:image/png;base64,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)
..............(ii)
dividing (i) by (ii)
![rightwards double arrow t a n squared A equals t a n squared B
rightwards double arrow t a n squared A minus t a n squared B equals 0
rightwards double arrow t a n left parenthesis A plus B right parenthesis t a n left parenthesis A minus B right parenthesis equals 0
rightwards double arrow A equals n pi plus-or-minus B left parenthesis n element of I right parenthesis](data:image/png;base64,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)
Again, sin A = sin B
![A equals n pi plus left parenthesis negative 1 right parenthesis to the power of n B](data:image/png;base64,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)
(∴A= nπ ± B accordingly n is even or odd integer)
And cos A = cos B
⇒ A = nπ ± B (n ∈ I)
Therefore, statement-I is true,
Now,
Statement-II: sinA = sinB and cosA = cosB, then ![A equals n pi plus B comma n element of I](data:image/png;base64,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)
Also, tanA = tanB
tanA − tanB = 0
tan(A−B) = 0
A−B=nπ
∴A=nπ+B (n∈I)
Therefore, Statement-II is also true and correct explanation of Statement-I.
Hence, the correct answer is Statement-I is true, Statement-II is true; Statement-II is NOT a correct explanation for Statement-I
In this question, we have to find the statements are the correct or not and statement 2 is correct explanation or not, is same as assertion and reason. Here, Start solving first Statement and try to prove it. Then solve the Statement-II.
Related Questions to study
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Arsine is:
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,
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In this question, we have to find the statements are the correct or not and statement 2 is correct explanation or not, is same as assertion and reason. Here, Start solving first Statement and try to prove it. Then solve the Statement-II. Always, the AM–GM inequality states that AM ≥ GM.
Statement-I : If sin x + cos x = then
Statement-II : AM ≥ GM
In this question, we have to find the statements are the correct or not and statement 2 is correct explanation or not, is same as assertion and reason. Here, Start solving first Statement and try to prove it. Then solve the Statement-II. Always, the AM–GM inequality states that AM ≥ GM.
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In this question, we have to find the statements are the correct or not and statement 2 is correct explanation or not, is same as assertion and reason. Here, -1 ≤ sinx ≤ 1 for all value, remember that.
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In this question, we have to find the statements are the correct or not and statement 2 is correct explanation or not, is same as assertion and reason. Here, -1 ≤ sinx ≤ 1 for all value, remember that.
if
if
if
if
if
if
if
if
if
In this question, we have to find the general solution of x. Here more than one option will correct. Remember the rules for finding the general solution.
if
In this question, we have to find the general solution of x. Here more than one option will correct. Remember the rules for finding the general solution.
Number of ordered pairs (a, x) satisfying the equation
is
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In the interval the equation
has
In this question, we have to find type of solution, here, we know if then we can take antilog, b = ca, and cos2 θ = 1 – 2 sin2 θ . Remember these terms and find the solution easily.
In the interval the equation
has
In this question, we have to find type of solution, here, we know if then we can take antilog, b = ca, and cos2 θ = 1 – 2 sin2 θ . Remember these terms and find the solution easily.