Match the following. List I List II (A) Number of roots of cos 7 x + sin 4 x = 1 in ( − π , π ) (P) 1 (B) 3 csc 2 0 ∘ − sec 2 0 ∘ (Q) 4 (C) 4 cos 3 6 ∘ − 4 cos 7 2 ∘ + 4 sin 1 8 ∘ cos 3 6 ∘ (R) 0 (D

Question

Match the following. List I List II (A) Number of roots of cos 7 x + sin 4 x = 1 in ( − π , π ) (P) 1 (B) 3 ​ csc 2 0 ∘ − sec 2 0 ∘ (Q) 4 (C) 4 cos 3 6 ∘ − 4 cos 7 2 ∘ + 4 sin 1 8 ∘ cos 3 6 ∘ (R) 0 (D) Number of x ∈ [ − 2 π , 2 π ] with csc x = 1 + cot x (S) 3 (T) 2

TestHub · Accepted Answer

A: x = -π/2, 0, π/2 (three). B: direct trigonometric simplification gives 4. C: standard exact values give 3. D: sin x + cos x = 1 with sin x ≠ 0 gives x = -3π/2, π/2 (two).

Mathematics - Trigonometric Equation Question with Solution | TestHub

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Doubts & Discussion

List I	List II
(A) Number of roots of $cos^{7} x + sin^{4} x = 1$ in $(- π, π)$	(P) 1
(B) $3 csc 2 0^{\circ} - sec 2 0^{\circ}$	(Q) 4
(C) $4 cos 3 6^{\circ} - 4 cos 7 2^{\circ} + 4 sin 1 8^{\circ} cos 3 6^{\circ}$	(R) 0
(D) Number of $x \in [- 2 π, 2 π]$ with $csc x = 1 + cot x$	(S) 3
	(T) 2