Write the values of x in -0- - for which sin 2 x - 1-2 and cos 2 x are in A-P-

We want to find the value of x for which 1/2 sin 2x=cos 2x 1/2 ⇒ cos 2x+sin 2x=1 ⇒ 1 2 sin^2 x+2 sin x cos x=1 ⇒ 2 sin x(cos x sin x)=0 ⇒ sin x=0 or cos x =sin ...

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Standard XII

Mathematics

Equations with Solutions at Boundary Values

Write the val...

Question

$Write the values of x in [0, π] f o r w h i c h s i n 2 x, \frac{1}{2} a n d c o s 2 x a r e i n A . P .$

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Solution

$We want to find the value of x for which \frac{1}{2} - s i n 2 x = c o s 2 x - \frac{1}{2} \Rightarrow c o s 2 x + s i n 2 x = 1 \Rightarrow 1 - 2 s i n^{2} x + 2 s i n x c o s x = 1 \Rightarrow 2 s i n x (c o s x - s i n x) = 0 \Rightarrow s i n x = 0 o r c o s x = s i n x \Rightarrow x = 0, \frac{π}{4}, π$

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Similar questions

Q. Write the values of x in [0, π] for which

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Write the values of x in[0,π]for which sin 2x,12 and cos 2x are in A.P.

We want to find the value of x for which 12−sin 2x=cos 2x−12⇒cos 2x+sin 2x=1⇒1−2 sin2x+2 sin x cos x=1⇒2 sin x(cos x−sin x)=0⇒sin x=0 or cos x =sin x⇒x=0,π4,π

$Write the values of x in [0, π] f o r w h i c h s i n 2 x, \frac{1}{2} a n d c o s 2 x a r e i n A . P .$