Question

Sin A = COS 2A then tan3A ​

Answer 1

$\Large{\boxed{\underline{\overline{\mathfrak{\star \: QuEsTiOn :- \: \star}}}}}$

↠ Sin A = COS 2A then tan3A

$\huge\underline{\overline{\mid{\bold{\pink{ANSWER-}}\mid}}}$

↠ Tan 3A = ∞

$\Large{\underline{\underline{\bf{Given:-}}}}$

↠ SinA = Cos2A

$\Large{\underline{\underline{\bf{Find:-}}}}$

↠ Tan3A

$\Large{\underline{\underline{\bf{SoLuTion:-}}}}$

↠All triangles have 3 angles that add to 180 degrees.

Therefore, if one angle is 90 degrees we can figure out

↠ Sin Theta = Cos (90 - Theta) and

↠ Cos Theta = Sin (90 - Theta).

↠ SinA = Cos2A

Now , Changing one out of them either Sin Theta into Cos (90 - Theta) or Cos Theta into Sin (90 - Theta).

❥ Cos(90 - A) = Cos2A

❥ 90 - A = 2A

❥ 2A + A = 90

❥ 3A = 90

❥ A = 90/3

❥ A = 30°

Putting the value of A

❥ Tan3A = Tan 3 × 30°

↠ Tan 90°

↠ ∞

$\mathfrak{\huge{\purple{\underline{\underline{Hence}}}}}$

$\boxed{\boxed{\bold{Therefore, \ the \ value \ of\ Tan3A \ = \ Tan90° }}}}$