If -sin 2 x-cos 2 x d x-1-2sin 2 x-c-a- then the value of a and c is

The correct option is A c=π/4 and a = k (an arbitrary constant)∫ (sin 2x+cos 2x)dx= cos 2x/2+sin 2x/2+k =1/√(2) ( sin 2x cos π/4 cos 2x sin π/4 )+k =1/√(2)sin ...

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Byju's Answer

Standard XII

Mathematics

Using Monotonicity to Find the Range of a Function

If ∫sin 2 x+c...

Question

If $\int (s i n 2 x + c o s 2 x) d x = \frac{1}{\sqrt{2}} s i n (2 x - c) + a$ , then the value of a and c is

c = \frac{π}{4}

and a = k (an arbitrary constant)

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c = \frac{- π}{4}

and

a = \frac{π}{2}

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c = \frac{π}{2}

and a is an arbitrary constant

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None of these

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Solution

The correct option is A $c = \frac{π}{4}$ and a = k (an arbitrary constant)
$\int (s i n 2 x + c o s 2 x) d x = - \frac{c o s 2 x}{2} + \frac{s i n 2 x}{2} + k$
$= \frac{1}{\sqrt{2}} (s i n 2 x c o s \frac{π}{4} - c o s 2 x s i n \frac{π}{4}) + k$
$= \frac{1}{\sqrt{2}} s i n (2 x - \frac{π}{4}) + k$
$\Rightarrow c = \frac{π}{4}$ and a = k, an arbitrary constant.

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If ∫(sin 2x+cos 2x)dx=1√2sin(2x−c)+a, then the value of a and c is

The correct option is A c=π4 and a = k (an arbitrary constant)∫(sin 2x+cos 2x)dx=−cos 2x2+sin 2x2+k =1√2(sin 2x cos π4−cos 2x sin π4)+k =1√2sin(2x−π4)+k ⇒c=π4 and a = k, an arbitrary constant.

If $\int (s i n 2 x + c o s 2 x) d x = \frac{1}{\sqrt{2}} s i n (2 x - c) + a$ , then the value of a and c is