Question

if sin A = cos A then tan A =?​

Answer 1

Answer:

ANSWER

Given, sinA=cosA

cosA

sinA

=1

⇒tanA=1

⇒A=45

∘

Step-by-step explanation:

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Answer 2

Given,

$\sin A = \cos A$.

To find,

$\tan A$.

Solution,

As we know that there are relations between all of the trigonometric functions.

Among all these, the relationship among $\sin A, \cos A,$ and $\tan A$ is given by,

$\tan A =\frac{\sin A}{\cos A}$

But according to the given condition, here,

$\sin A = \cos A$

Substituting this given value in the above relation, we get,

$\tan A =\frac{\sin A}{\sin A}$

⇒ $\tan A =1$

As $\tan A$ is = 1, here, we can find the angle A as well, which will be

$A=\tan^{-1}(1)$

⇒ A = 45°.

Therefore, when $\sin A = \cos A,$ the value of $\tan A =1.$