Easy Sec and Cosec!

Geometry Level 2

If sec ⁡ 4 A = csc ⁡ ( A − 2 0 ∘ ) \sec 4A = \csc (A-20^{\circ}) , where 4 A 4A is an acute angle, then find the value of A A .

40 100 20 22 110

Anish Harsha by Anish Harsha , 20, India

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1 solution

Anish Harsha
Mar 22, 2016

It is given that , sec ⁡ 4 A = csc ⁡ ( A − 2 0 ∘ ) \color{#D61F06}{\sec 4A} = \color{#3D99F6}{\csc (A-20^{\circ})}

Since, sec ⁡ θ = csc ⁡ ( 90 − θ ) \color{#EC7300}{\sec \theta = \csc (90-\theta)} = csc ⁡ ( 9 0 ∘ − 4 A ) = csc ⁡ ( A − 20 ) \color{#D61F06}{= \csc(90^{\circ} - 4A)} = \color{#3D99F6}{\csc(A-20)} = 9 0 ∘ − 4 A = A − 2 0 ∘ \color{#D61F06}{= 90^{\circ} -4A}=\color{#3D99F6}{A-20^{\circ}} = 9 0 ∘ + 2 0 ∘ = A + 4 A \color{#D61F06}{= 90^{\circ} + 20^{\circ}} =\color{#3D99F6}{ A+4A} = A = 110 5 = 2 2 ∘ \color{#D61F06}{= A= \dfrac{110}{5}} = \color{magenta}{22^{\circ}}

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