Trigonometric Identities

JEE Main Mathematics · 6 questions

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• 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 tan A, tan B, where A, B ∈(-(π)/2, (π)/2), be the roots of the quadratic equation x^2-2 x-5=0. Then 20 sin^2((A+B)/2) is…20265 April, Shift 1 · Q6
• If A=(sin 3^°)/(cos 9^°)+(sin 9^°)/(cos 27^°)+(sin 27^°)/(cos 81^°) and B= tan 81^°- tan 3^°, then B/A is equal to ____.20264 April, Shift 1 · Q23
• Let a_k=( tan θ_k) i+ j and b_k= i-( cot θ_k) j, where θ_k=(2^k-1 π)/(2^n+1), for some n ∈ N, n>5. Then the value of (Σ_k=1^n|…20264 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
• If sin ((π)/18) sin ((5 π)/18) sin ((7 π)/18)=K, then the value of sin ((10 K π)/3) is:20262 April, Shift 1 · Q11