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If tan (4A + 50°) = cot A, where A and 4A + 50° are acute angles.

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Find A.?

asked May 27, 2013 in TRIGONOMETRY by anonymous Apprentice

1 Answer

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if A and 4A + 50º are acute angle means less than 90º

tan(4A + 50º) = cotA

Let A = 90 - θ

Take cot trigonometric function  to each side

cotA = cot(90 - θ) = tanθ

But tan(4A + 50º) = cotA = tanθ

Remove tan function to each side

4A + 50º = θ -----------(1)

4(90 - θ) + 50º = θ

360º - 4θ + 50º = θ

410º - 4θ = θ

5θ = 410º

θ = 82º------------------(2)

We rewrite the equations from (1) and (2)

4A + 50º = 82º

4A = 32º

A = 8º.

answered May 27, 2013 by diane Scholar

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