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

1 21/4cosx=−sinx2sin2x+sinx−2=02 sinx−1sinx+2=0 sinx=12 x∈θ2x=3π42 1−tan2θtanθ−12=0tanθ=tanπ4θ=nπ±π4,n∈z3 1+tan2x1−tan2x=2cos2x=12cos2x=cosπ4x=nπ±π84 tan5θ=tanπ2−2θ5θ=nπ+π2−2θθ=nπ7+π14 n≠3,10,17 where Tan5θ is not defined

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

1 21/4cosx=−sinx2sin2x+sinx−2=02 sinx−1sinx+2=0 sinx=12 x∈θ2x=3π42 1−tan2θtanθ−12=0tanθ=tanπ4θ=nπ±π4,n∈z3 1+tan2x1−tan2x=2cos2x=12cos2x=cosπ4x=nπ±π84 tan5θ=tanπ2−2θ5θ=nπ+π2−2θθ=nπ7+π14 n≠3,10,17 where Tan5θ is not defined

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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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