If `sinα=1/2` and `cosβ=1/2 `find α+β

If cos(α−β)=1 and cos(α+β)= 1/e , where α, β∈[−π,π]. Then number of ordered pairs of (α,β) is

If cosα+cosβ= 3/2 ​ and sinα+sinβ= 1/2 ​ and θ is the arithmetic mean of α and β, then sin2θ+cos2θ is equal to

If cosα+cosβ= 3/2 ​ and sinα+sinβ= 1/2 ​ and θ is the arithmetic mean of α and β, then sin2θ+cos2θ is equal to

The number of ordered pairs (α,β), where α,β∈(−π,π) satisfying cos (α−β)=1 and cos(α+β)=1/e is

cosα+cosβ= 3/2 ​ and sinα+sinβ= 1/2 ​ and θ is the arithmetic mean of α and β, then sin2θ+cos2θ is equal to Yes No

If sin(120° – α) = sin(120° – β) and 0 < α, β < π then find the relation between α and β.

If sinα.sinβ − cosα.cosβ + 1 = 0 then show that 1 + cotα.tanβ = 0

The angle of elevation of the top of a hill from each of the verticles A,B,C of a horizontal triangle is alpha . The height of the hill is 1. b tan α cosec β 2. 1 2 a tan α cosec A 3. 1 2 c tan α cos e c C 4. none of these

If 32tan ^8 θ=2cos^2 α−3cosα and 3cos2θ=1 then the general value of α is

If a^2 + (1)/( a^2 ) = 2 , find : (i) a+ (1)/( a)