Question
Download Solution PDFFind general solution of tan x = \(\sqrt 3\)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
General solution of some standard trigonometric equations:
|
Equations |
Solutions |
Conditions |
|
sin θ = sin α |
θ = nπ + (-1)n α |
α ∈ [-π/2, π/2] and n ∈ z |
|
cos θ = cos α |
θ = 2nπ ± α |
α ∈ [0, π] and n ∈ z |
|
tan θ = tan α |
θ = nπ + α |
α ∈ (-π/2, π/2) and n ∈ z |
Calculation:
Given: tan x = \(\sqrt 3\)
⇒ tan x = tan \(\rm \frac {\pi}{3}\)
As we know, If tan θ = tan α then θ = nπ + α
Therefore, x = nπ + \(\rm \frac {\pi}{3}\)
Hence, the general solution of tan x = \(\sqrt 3\) is nπ + \(\rm \frac {\pi}{3}\), n ∈ Z.
Last updated on Jun 11, 2025
-> The Indian Army has released the official notification for the post of Indian Army Havildar SAC (Surveyor Automated Cartographer).
-> Interested candidates had applied online from 13th March to 25th April 2025.
-> Candidates within the age of 25 years having specific education qualifications are eligible to apply for the exam.
-> The candidates must go through the Indian Army Havildar SAC Eligibility Criteria to know about the required qualification in detail.