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Trigonometric EquationsGeneral Solutions1. tan x = 2P. 2nπ±2π3,nI2. sin x = 32Q. nππ4,nI3. cos x =12R. nπ+(1)nπ3,nI4. cot x = -1S. nπ+tan1(2),nI


A

1 - R, 2 - S, 3 - Q, 4 - P

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B

1 - R, 2 - S, 3 - P, 4 - Q

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C

1 - S, 2 - R, 3 - Q, 4 - P

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D

1 - S, 2 - R, 3 - P, 4 - Q

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Solution

The correct option is D

1 - S, 2 - R, 3 - P, 4 - Q


The expression involving an integer 'n' which gives all solutions of a trigonometric equation is called general solution.

1. tan x = 2

tan x = tan {tan1 (2) }

General solution when tan x = tan α

x = nπ + α

So general solution is x = nπ + tan1 (2) n ∈ I

2. sin x = 32

sin x = sin π3

x = nπ + (1)n π3 n ∈ I

3. cos x = - 12

cos x = cos 2π3

x = 2nπ ± 2π3 n ∈ I

4. cot x = -1

cot x = cot(- π4)

x = nπ - π4 n ∈ I


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