Compound angles

JEE Main Mathematics · Trigonometric Identities · 10 questions, latest first

• 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 (tan (A-B))/(tan A)+(sin^2 C)/(sin^2 A)=1, A, B, C ∈(0, (π)/2), then202628 January, Shift 1 · Q12
• If cot x=5/12 for some x ∈(π, (3 π)/2), then sin 7 x( cos (13 x)/2+ sin (13 x)/2)+ cos 7 x( cos (13 x)/2- sin (13 x)/2) is equal…202624 January, Shift 1 · Q12
• Let (π)/2<θ<π and cot θ=-1/(2 √2). Then the value of sin ((15 θ)/2)( cos 8 θ+ sin 8 θ)+ cos ((15 θ)/2)( cos 8 θ- sin 8 θ) is…202623 January, Shift 2 · Q14
• Let cos (α+β)=-1/10 and sin (α-β)=3/8, where 0<α<(π)/3 and 0<β<(π)/4. If tan 2 α=(3(1-r √5))/(√11(s+√5)), r, s ∈ N, then r+s is…202622 January, Shift 2 · Q23
• If (cos^2 48^°- sin^2 12^°)/(sin^2 24^°- sin^2 6^°)=(α+β √5)/2, where α, β ∈ N, then α+β is equal to ____202622 January, Shift 1 · Q24
• The value of cosec 10^°-√3 sec 10^° is equal to:202621 January, Shift 1 · Q13
• The value of ( sin 70^°)( cot 10^° cot 70^°-1) is202523 January, Shift 1 · Q11
• If tan A=1/(√(x(x^2+x+1))), tan B=(√x)/(√(x^2+x+1)) and tan C=(x^-3+x^-2+x^-1)^1 / 2, 0<A, B, C<(π)/2, then A+B is equal to:20241 February, Shift 1 · Q20
• For α, β ∈(0, π / 2), let 3 sin (α+β)=2 sin (α-β) and a real number k be such that tan α=k tan β. Then, the value of k is equal to202430 January, Shift 2 · Q11