Tiêu đề TRIGONOMETRY - 3.pdf ✅

b) 2nπ + 7π 4 c) nπ + (−a) n 7π 4 d) 7nπ 4 , n ∈ z INTEGER ANSWER TYPE: 5. If tan θ + sec θ = √3, then the principal value of (θ + π 6 ) is = π k then k = JEE MAIN LEVEL-2 6. If 3tan (θ − 15∘ ) = tan (θ + 15∘ ), 0 < θ < π, then θ = a) π 2 b) π 4 c) π 6 d) π 3 7. If tan mθ = cot nθ, then G.S of θ = a) (k+a)π 2( m+n) , ∀k ∈ z b) (2k+a)π 2( m+n) , ∀k ∈ z c) (2k+a)π m+n , ∀k ∈ z d) (2k+a)π m−n , ∀k ∈ z 8. If sin x ⋅ sin (60∘ + x) ⋅ sin (60∘ − x) = 1 8 , then x = a) nπ + (−a) n ⋅ π 6 b) nπ 3 + (−a) n ⋅ π 18 c) nπ + (−a) n ⋅ π 3 d) nπ 3 + (−a) n ⋅ π 9 9. If √sin x + cos x = 0 then sin x = a) √5+1 2 b) √5+1 8 c) √5−1 8 d) √5−1 2 10. If 3cos 2θ + 2 = 7sin θ, then θ = a) nπ + (−a) n π 4 , n ∈ z b) nπ + (−a) n π 6 , n ∈ z c) nπ + (−a) n+1 π 6 , n ∈ z( or )nπ + (−a) n π 3 , n ∈ z d) nπ + (−a) n π 2 , n ∈ z( or )nπ + (−a) n π 6 , n ∈ z 11. The solution set of tan x + tan (120∘ + x) + tan (120∘ − x) = 0 is a) nπ 3 , ∀n ∈ z b) nπ 6 , ∀n ∈ Z c) nπ 4 , ∀n ∈ z d) nπ 2 , ∀n ∈ z 12. If cos3 α + cos3 (120∘ + α) + cos3 (120∘ − α) = 3√3 4 , then α is a) φ b) 2nπ ± π 3 , n ∈ z c) (2n + a) π 2 n ∈ z d) nπ, n ∈ z 13. If sin (x + 28∘ ) = cos (3x − 78∘ ), then x = a) 370 , 8 0 b) 39∘ c) 350 , 8 0 d) 47∘ JEE MAIN LEVEL - 3 14. If 2 + √3sec x − 4cos x = 2√3, then θ = a) 2nπ ± 2π 3 , n ∈ z b) 2nπ ± π 3 , n ∈ z (or) 2nπ ± 5π 6 , n ∈ z c) (2n + a)π, n ∈ z (or) 2nπ ± π 3 , n ∈ z d) 2nπ: n ∈ z (or) 2nπ ± π 3 , n ∈ z 15. If cos 3θ 2cos 2θ−1 = 1 2 , then a) θ = nπ + π 3 b) θ = 2nπ ± π 3 c) θ = 2nπ ± π 6 , n ∈ z d) θ = nπ ± π 6 , n ∈ z 16. If cos 20∘ = k and cos x = 2k 2 − 1, then the possible values of x between 0 ∘ and 360∘ are a) 140∘ b) 40∘&140∘ c) 40∘&320∘ d) 50∘&130∘ JEE MAIN LEEL -4 17. The number of real solutions of the equations cos2 x + sin3 x = 1 in the interval [0,2π] is a) 4