Question

Sin A = cos A , Tan A = ?

Answer 1

Answer:

$\gray{\mathsf{Tan\:A = 1}}$

Solution:

$\Large{\boxed{\pink{\mathsf{Given\:that:}}}}$

$\green{\mathsf{sin\:A = cos\:A}}$

$\Large{\boxed{\blue{\mathsf{We\:know\:that:}}}}$

$\large{\mathsf{\frac{sin\:\theta}{cos\:\theta} = tan\:\theta}}$

$\large{\mathsf{\implies \therefore \frac{sin\:A}{cos\:A} = tan\:A}}$

$\large{\mathsf{\implies \frac{sin\:A}{sin\:A} = tan\:A}}$

$\red{\mathsf{[∵\:given\:that: sin\:A = cos\:A] }}$

$\large{\mathsf{\implies \therefore \frac{\cancel{sin\:A}}{\cancel{sin\:A}} = tan\:A}}$

$\large{\implies{\orange{\therefore tan\:A = 1}}}$

$\LARGE{\purple{\boxed{\mathsf{tan\:A = 1}}}}$

Answer 2

Step-by-step explanation:

$\huge\bf{\mid{\overline{\underline{ANSWER:-}}\mid}}$

$\huge\bold{GIVEN:-} \\ \\ \red{ \sin(A) = \cos(A)} \\ \\ dividing \: both \: sides \; by \: \cos(A) \implies \\ \\ \frac{\sin(A)}{\cos(A)} = \frac{\cos(A)}{\cos(A)} \\ \\ \tan(A) = 1........(\frac{\sin(A)}{\cos(A)} = \tan(A) ) \\ \\\huge{\boxed{\boxed{ \blue{ \therefore \tan(A) = 1 }}}}$