Question
Download Solution PDFtan x = \(\sqrt 3\) का सामान्य हल ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
कुछ मानक त्रिकोणमितीय समीकरणों का सामान्य हल:
|
समीकरण |
हल |
शर्त |
|
sin θ = sin α |
θ = nπ + (-1)n α |
α ∈ [-π/2, π/2] और n ∈ z |
|
cos θ = cos α |
θ = 2nπ ± α |
α ∈ [0, π] और n ∈ z |
|
tan θ = tan α |
θ = nπ + α |
α ∈ (-π/2, π/2) और n ∈ z |
गणना:
दिया गया है: tan x = \(\sqrt 3\)
⇒ tan x = tan \(\rm \frac {\pi}{3}\)
चूँकि हम जानते हैं, यदि tan θ = tan α है, तो θ = nπ + α है।
इसलिए, x = nπ + \(\rm \frac {\pi}{3}\)
अतः tan x = \(\sqrt 3\) का सामान्य हल nπ + \(\rm \frac {\pi}{3}\), n ∈ Z है।
Last updated on Jul 1, 2025
-> The Indian Army has released the Exam Date for Indian Army Havildar SAC (Surveyor Automated Cartographer).
->The Exam will be held on 9th July 2025.
-> 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.
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