Question

If sinA =cosA then find the value of A ​

Answer 1

Answer:

SinA = CosA

SinA = Sin(90-A)

A=90-A

2A=90

A=45°

Answer 2

Answer:

$\large{\underline{\boxed{\sf A =45^{\circ}}}}$

Step-by-step explanation:

There are two methods to solve the problem ;

Method I: Using identity

Given that ;

$\sin (\text{A}) = \cos (\text A)$

Now, we know that ;

• CosA = Sin(90 - A)

On substituting the value of CosA in the above, we get -

⇒ $\sin (\text A) = \sin (90 - \text A)$

On cancelling sin from both the sides -

⇒ $\cancel{\sin} (\text A) = \cancel{\sin} (90 - \text A)^{\circ}$

⇒ $\text A = 90 - \text A$

⇒ $\rm A + A = 90$

⇒ $\rm 2A = 90$

⇒ $\text A = \dfrac{90}{2}$

⇒ $\text A = 45^{\circ}$

Thus, the value of A is 45°

$\rule{300}{2}$

Method II : Hit-and-Trial

$\sin (\text A) = \cos(\text A)$

(i) Put A = 45° in the above,

⇒ $\sin 45^{\circ} = \cos 45^{\circ}$

We know that,

• Sin 45° = 1/√2
• Cos 45° = 1/√2

On substituting the value in the above,

⇒ $\tt \dfrac{1}{\sqrt{2}} = \dfrac{1}{\sqrt{2}}$

Thus, the value of A is 45°