Question

If sin2A=1, then find the value of tanA​

Answer 1

Answer:

1

Step-by-step explanation:

sin2A=1

sin2A=sin90

2A=90

A=45

tanA=tan45

tanA=1

Answer 2

Given:

$sin2A=1$

To find: the value of $tanA$.

Solution:

Solve the given expression.

$\[\begin{array}{l}\sin 2A = 1\\ \Rightarrow \sin 2A = \sin {90^ \circ }\\ \Rightarrow {\sin ^{ - 1}}\left( {\sin 2A} \right) = {\sin ^{ - 1}}\left( {\sin {{90}^ \circ }} \right)\\ \Rightarrow 2A = {90^ \circ }\end{array}\]$

$\[\begin{array}{l} \Rightarrow A = \frac{{{{90}^ \circ }}}{2}\\ \Rightarrow A = {45^ \circ }\end{array}\]$

Find the value of $tanA$.

$\[\tan A = \tan {45^ \circ }\]$

$\[ \Rightarrow \tan A = 1\]$

Hence, the value of $tanA$ is 1.