Question

if x is in first quadrant and sinx= cosx,then what is the value of x?​

Answer 1

The value of x is "$\dfrac{\pi}{4}$".

Step-by-step explanation:

We have,

$\sin x = cos x$

⇒$\sin x = sin( \frac{\pi}{2} - x)$

⇒ x = $\frac{\pi}{2} - x$

⇒ x + x =$\dfrac{\pi}{2}$

⇒ 2x =$\dfrac{\pi}{2}$

⇒ x = $\dfrac{\pi}{4}$ or 45°

∵ $\dfrac{\pi}{4}$ lies  in first quadrant.

Hence, the value of x is  "$\dfrac{\pi}{4}$".

Answer 2

Answer:

The value of x is 45°

Step-by-step explanation:

Given expression,

sin x = cos x

We know that cos a = sin (90 - a)

⇒ sin x = sin (90 - x)

⇒ x = 90 - x

⇒ x + x = 90

⇒ 2x = 90

⇒ x = $\frac{90}{2}$ = 45

Hence, the value of x would be 45°

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