HSC Arts 12th Board ExamMaharashtra State Board
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# Find the general solution of cot x + tan x = 2 cosesc x. - HSC Arts 12th Board Exam - Mathematics and Statistics

ConceptTrigonometric Functions General Solution of Trigonometric Equation of the Type

#### Question

Find the general solution of cot x + tan x = 2 cosesc x.

#### Solution

cot x + tan x = 2 cosesc x

cosx/sinx+sinx/cosx=2/sinx

(cos^2x+sin^2x)/(sinx.cosx)=2/sinx

1/(sinx.cosx)=2/sinx ...................[because cos^2x+sin^2x=1]

1=2/sinx xx sinx.cosx

1=2cosx

cosx=1/2

x=cos^-1(1/2)=pi/3

Since, cos θ= cos α implies theta=2npi+-alpha,n in Z

the required general solution is x=2npi+-pi/3 where n in Z

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Solution Find the general solution of cot x + tan x = 2 cosesc x. Concept: Trigonometric Functions - General Solution of Trigonometric Equation of the Type.
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