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Find the general solution of the following equation: tan θ = - 1

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प्रश्न

Find the general solution of the following equation:

tan θ = - 1

योग
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उत्तर

The general solution of tan θ = tan α is
θ = nπ + α, n ∈ Z.
Now, tan θ  =  – 1 

∴ tan θ  = - tan  `pi/(4)  .....[ ∵ tan  pi/4 = 1]`        

∴ tan θ = `tan(pi - pi/4)`  ...[ ∵ tan(π - θ) = – tan θ] 

∴ tan θ = `tan  (3pi)/(4)`         

∴ the required general solution is
θ = nπ + `(3pi)/(4)`, n ∈ Z.

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अध्याय 3: Trigonometric Functions - Exercise 3.1 [पृष्ठ ७५]

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बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 12 Maharashtra State Board
अध्याय 3 Trigonometric Functions
Exercise 3.1 | Q 4.3 | पृष्ठ ७५

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