Maximum and minimum values

JEE Main Mathematics · Trigonometric Identities · 8 questions, latest first

• For the functions f(θ)=α tan^2 θ+β cot^2 θ, and g(θ)=α sin^2 θ+β cos^2 θ, α>β>0, let min_0<θ<(π)/2 f(θ)= max_0<θ<π g(θ). If the…20266 April, Shift 1 · Q24
• Let P={θ ∈[0,4 π]: tan^2 θ ≠ 1} and S={a ∈ Z: 2( cos^8 θ- sin^8 θ) sec 2 θ=a^2, θ ∈ P}. Then n(S) is:20262 April, Shift 2 · Q13
• The least value of ( cos^2 θ-6 sin θ cos θ+3 sin^2 θ+2) is202623 January, Shift 2 · Q18
• Let α and β respectively be the maximum and the minimum values of the function f(θ)=4( sin^4((7 π)/2-θ)+ sin^4(11 π+θ))-2(…202623 January, Shift 1 · Q13
• Let the range of the function f(x)=1/(2+ sin 3 x+ cos 3 x), x ∈ R be [a, b]. If α and β are respectively the A.M. and the G.M. of…20249 April, Shift 2 · Q1
• If the range of f(θ)=(sin^4 θ+3 cos^2 θ)/(sin^4 θ+ cos^2 θ), θ ∈ R is [α, β], then the sum of the infinite G.P., whose first term…20248 April, Shift 1 · Q21
• Let f(x)=1/(7- sin 5 x) be a function defined on R. Then the range of the function f(x) is equal to:20246 April, Shift 2 · Q1
• Let f: R → R be a function defined by f(x)= log_√m{√2( sin x- cos x)+m-2}, for some m, such that the range of f is [0,2]. Then…202325 January, Shift 2 · Q61