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Question

Assertion :Statement 1: The value of x for which (sinx+cosx)1+sin2x=2 when 0xπ is π4 only Reason: Statement 2: The maximum value of sinx+cosx occurs when x=π4

A
if both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1
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B
if both the statements are TRUE and STATEMENT 2 is NOT the correct explanation of STATEMENT 1
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C
if STATEMENT 1 is TRUE and STATEMENT 2 is FALSE
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D
if STATEMENT 1 is FALSE and STATEMENT 2 is TRUE
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Solution

The correct option is A if both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1
Let D=sinx+cosx
dDdx=cosxsinx=0
cosx=sinx
tanx=1=tanπ4
x=nπ+π4
in 0x4
x=π4
[d2xdx2]x=π4=sinxcosx<0
sinx+cosx is maximum at π4
Statement 2 is correct.
M=(sinx+cosx)1+sin2x
=(sinx+cosx)(sinx+cosx)2
If x=π4
M=(2)2=2
Statement 1 is correct.
Statement 2 is the correct reason for Statement 1 because in that case only the value of (sinx+cosx)1+sin2x is maximum.

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