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If sin x = cos $(2x – 10^\circ)$, find the Value of x.

If sin x = cos $(2x – 10^\circ)$, find the Value of x.
यदि sin x = cos $(2x – 10^\circ)$, हो , तो x का मान ज्ञात कीजिए।

$25.52^\circ$ $33.33^\circ$ $40^\circ$ $50^\circ$

Detailed Solution & Logic

Correct Answer:

$33.33^\circ$

दिया है:
$\sin x = \cos(2x - 10^\circ)$

हम जानते हैं कि
$\cos \theta = \sin(90^\circ - \theta)$

तो,
$\cos(2x - 10^\circ) = \sin(100^\circ - 2x)$

अब समीकरण:
$\sin x = \sin(100^\circ - 2x)$

⇒ या तो $x = 100^\circ - 2x$

$3x = 100^\circ$
$x = 33.33^\circ$

$33.33^\circ$

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