Question
Statement - I The value of x for which (sin x + cos x)1 + sin 2x = 2, when 0 ≤ x ≤ , is only.
Statement - II The maximum value of sin x + cos x occurs when x =
Statement-I is true, Statement-II is true ; Statement-II is 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
Statement-I is true, Statement-II is true ; Statement-II is correct explanation for Statement-I.
Statement-I is true, Statement-II is true ; Statement-II is NOT a correct explanation for Statement-I.
Hint:
Here two statements are given. 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 true ; Statement-II is correct explanation for Statement-I.
Here we have to find the which statement is correct and if its correct explanation or not.
Firstly, statement 1: The value of x for which
= 2, when 0 ≤ x ≤, is
only.
So, we have,
=
[ since, sin2x + cos2x = 1 and sin2x = 2sinx.cosx]
=
[ a2 + b2 + 2ab = (a+b)2]
Now , at x =
, we have,
=![open parentheses sin straight pi over 4 plus cos straight pi over 4 close parentheses to the power of open parentheses sin straight pi over 4 plus cos straight pi over 4 close parentheses squared end exponent](data:image/png;base64,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)
=![open parentheses fraction numerator 1 over denominator square root of 2 end fraction plus fraction numerator 1 over denominator square root of 2 end fraction close parentheses to the power of open parentheses fraction numerator 1 over denominator square root of 2 end fraction plus fraction numerator 1 over denominator square root of 2 end fraction close parentheses squared end exponent](data:image/png;base64,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)
= ![open parentheses fraction numerator 2 over denominator square root of 2 end fraction close parentheses to the power of open parentheses fraction numerator 2 over denominator square root of 2 end fraction close parentheses squared end exponent](data:image/png;base64,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)
= ![open parentheses square root of 2 close parentheses to the power of open parentheses square root of 2 close parentheses squared end exponent](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEcAAAAZCAYAAABjNDOYAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAWNPAnzwAAAshJREFUeNrtWE1IVFEUfkiIyBAGgQwEhYgMEW1KKCokkBBx6cKhZhODSLRwqVDULogwqBBCwV0LSQsRXYpIRC1MWgVRLSJaCBUGFgNl34XvwfO++9/DedR88MHMvDfnnXPu+c4970ZRAzGugFvgR3CgkY7duA02g+fAT/9SYG3gGrjjSBP2gT91FyfBi3sYWAV88Jc2LoHLGflzFZzQJaZSh5Wv8NkqlMEpy/+fgFWP503Rrozz4AKrZxdEE5qtozQeKxphK/gO3G+R1HfwYOK3WD418BnYKf2nQLuFxG9d4CL7TgobYCkgqIKH1k36L9GHJEZ0Je4oqSbuQuuKaxO0H2OFCUqhG1wNXPEhGs4Cq/TFVE0hklI12AHal6st1bSvg+OBAS176t0E4cONxPdNSitZpTZJyejRLHwL+MXFqXmwPyAY4dRXi3M+6KcvMWqJz71c0eMeu1SRPafDo6JS+AC2BwQzwrKWcYYlu8UANxzHgyJ9USVnDHwNvneUVNxgi55yS2GbzcsXotcManpHOSGDo1zBssVeE33RySr2ddQiKZGQJcsuJ2T1zSXInYDEHKHzLY73H+bK21CzNOQqE3TZIKklh51XbsiZJmfMYTgLKeOa9DJ4R3HPG/pcNcRje2WQt/JMZfUK7PO4/zSl5SMr3RDYxYBDNwLVEBjUkFUGjoGfVWO2Qd8v2KhNaJcacvz68FBxb18UjkmH/mfcysXIPcMVOitduwXedbR9AHwKXgjYynMB1RB4jckRc8xLRaWddLDbwcR0Bg6BucAJnofoTsh+J2R3CnzrIKkSG3arhx9r9CV3WDdsf6JJPuLn++BNh94x69GTdC+euUEvzzJUmAZ/MNhNhxliMeANf4HnKbmFmCmGNWcmv8A58Lnj3ORzRDmsmWdyh3uR+jQwPqMdzfh5WRyT1h3dTM6hqAElBv+nYP8AEP29yNZy1o8AAAC7dEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdXA+PG1mZW5jZWQ+PG1zcXJ0Pjxtbj4yPC9tbj48L21zcXJ0PjwvbWZlbmNlZD48bXN1cD48bWZlbmNlZD48bXNxcnQ+PG1uPjI8L21uPjwvbXNxcnQ+PC9tZmVuY2VkPjxtbj4yPC9tbj48L21zdXA+PC9tc3VwPjwvbWF0aD4b2WoGAAAAAElFTkSuQmCC)
= ![open parentheses square root of 2 close parentheses squared](data:image/png;base64,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)
= 2
Therefore,
= 2 is True.
Now for statement 2 – The maximum value of sinx + cosx occur when x =
,
Let y = sinx + cosx
= cosx – sinx
= 0
cosx = sinx ,
tanx = 1 = tan ![straight pi over 4](data:image/png;base64,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)
we know, x = n π + ![straight pi over 4](data:image/png;base64,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)
in 0 ≤ x ≤ ![straight pi over 4](data:image/png;base64,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)
x = ![straight pi over 4](data:image/png;base64,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)
= -sinx – cosx < 0
therefore, sinx + cosx is maximum at π/4. And statement 2 is correct explanation because √2 is maximum value in π/4. And it is the only case which satisfies the statement 1 at π/4.
The correct answer is Statement-I is true, Statement-II is true; Statement-II is 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.
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