Match the column - I with column - II (column-I) Trigonometric equation Column(II) General solution(A)sinx+21/4cosx=0(I)P) θ=nπ7+π14 where n∈Z, n≠3,10,17,....(B)Solution of cot2θ=cot2θ−tan2θ(II)nπ±π8,n∈z(C)The general solution of sec2x=21−tan2x(III)nπ±π4,n∈z(D)Tan5θ=cot2θ Then θ=(IV)2nπ+3π4,n∈z

A → I V , B → I I I , C → I I , D → I

Match the column - I with column - II (column-I) Trigonometric equation Column(II) General solution(A)sinx+21/4cosx=0(I)P) θ=nπ7+π14 where n∈Z, n≠3,10,17,....(B)Solution of cot2θ=cot2θ−tan2θ(II)nπ±π8,n∈z(C)The general solution of sec2x=21−tan2x(III)nπ±π4,n∈z(D)Tan5θ=cot2θ Then θ=(IV)2nπ+3π4,n∈z

A → I V , B → I I I , C → I I , D → I

A → I , B → I I I , C → I V , D → I I

A → I V , B → I I I , C → I I , D → I

A → I , B → I V , C → I I , D → I I I

A → I V , B → I , C → I I I , D → I I

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Match the column - I with column - II
(column-I) Trigonometric equation Column(II) General solution
(A) $\sqrt{\sin x} + 2^{1 / 4} \cos x = 0$ (I) P) $θ = \frac{n π}{7} + \frac{π}{14}$ where $n \in Z$ , $n \neq 3, 10, 17, . . . .$
(B) Solution of $\cot 2 θ = \cot^{2} θ - \tan^{2} θ$ (II) $n π \pm \frac{π}{8}, n \in z$
(C) The general solution of $\sec^{2} x = \sqrt{2} (1 - \tan^{2} x)$ (III) $n π \pm \frac{π}{4}, n \in z$
(D) $T a n 5 θ = \cot 2 θ$ Then $θ =$ (IV) $2 n π + \frac{3 π}{4}, n \in z$

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$A \to I, B \to I I I, C \to I V, D \to I I$

$A \to I V, B \to I I I, C \to I I, D \to I$

$A \to I, B \to I V, C \to I I, D \to I I I$

$A \to I V, B \to I, C \to I I I, D \to I I$

answer is B.

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Detailed Solution

$(1) 2^{1 / 4} \cos x = - \sqrt{\sin x}$

$\sqrt{2} \sin^{2} x + \sin x - \sqrt{2} = 0$

$(\sqrt{2} \sin x - 1) (\sin x + \sqrt{2}) = 0$

$\sin x = \frac{1}{\sqrt{2}}$ $x \in θ_{2}$

$x = \frac{3 π}{4}$

$(2) (1 - \tan^{2} θ) {(\tan θ - 1)}^{2} = 0$

$\tan θ = \tan \frac{π}{4}$

$θ = n π \pm \frac{π}{4}, n \in z$

$(3) \frac{1 + \tan^{2} x}{1 - \tan^{2} x} = \sqrt{2}$

$\cos 2 x = \frac{1}{\sqrt{2}}$

$\cos 2 x = \cos \frac{π}{4}$

$x = n π \pm \frac{π}{8}$

$(4) \tan 5 θ = \tan (\frac{π}{2} - 2 θ)$

$5 θ = n π + \frac{π}{2} - 2 θ$

$θ = \frac{n π}{7} + \frac{π}{14}$ $n \neq 3, 10, 17$ where $Tan 5 θ$ is not defined

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	(column-I) Trigonometric equation		Column(II) General solution
(A)	$\sqrt{\sin x} + 2^{1 / 4} \cos x = 0$	(I)	P) $θ = \frac{n π}{7} + \frac{π}{14}$ where $n \in Z$ , $n \neq 3, 10, 17, . . . .$
(B)	Solution of $\cot 2 θ = \cot^{2} θ - \tan^{2} θ$	(II)	$n π \pm \frac{π}{8}, n \in z$
(C)	The general solution of $\sec^{2} x = \sqrt{2} (1 - \tan^{2} x)$	(III)	$n π \pm \frac{π}{4}, n \in z$
(D)	$T a n 5 θ = \cot 2 θ$ Then $θ =$	(IV)	$2 n π + \frac{3 π}{4}, n \in z$