Question

If 3cotA = 4tanA and A is an acute angle then what will be the value of secA?​

Answer 1

Given:

\mathsf{3\;tanA=cotA}3tanA=cotA

\underline{\textbf{To find:}}

To find:

\textsf{The angle A}The angle A

\underline{\textbf{Solution:}}

Solution:

\mathsf{Consider,}Consider,

\mathsf{3\;tanA=cotA}3tanA=cotA

\implies\mathsf{3\;tanA=\dfrac{1}{tanA}}⟹3tanA=

tanA

1

\implies\mathsf{tan^2A=\dfrac{1}{3}}⟹tan

2

A=

3

1

\implies\mathsf{tanA=\pm\dfrac{1}{\sqrt3}}⟹tanA=±

3

1

\mathsf{Since\;A\;is\;acute,\;tanA\;is\;positive}SinceAisacute,tanAispositive

\implies\mathsf{tanA=\dfrac{1}{\sqrt3}}⟹tanA=

3

1

\implies\boxed{\mathsf{A=30^\circ}}⟹

A=30

∘

Answer 2

Step-by-step explanation:

sec²A=1+tan²A

so SecA=√7/2