The equation sinx + sin2x + 2sinxsin2x
= 2cosx + cos2x is satisfied by values
of x for which
(1) x = nπ + (−1)^n (π/6) , n ∈ I
(2) x = 2nπ + ((2π)/3) , n ∈ I
(3) x = 2nπ − ((2π)/3) , n ∈ I
(4) x = 2nπ − (π/2) , n ∈ I
A mango in a tree is located (30,40) from the
point of projection of stone.Find the
minimum speed and the angle of projevtion
of the stone so as to hit the mango
ai) If θ is the angle in the fourth quadrant satisfying the equation : cot^2 θ = 4
find the value of the function: f(θ) = (1/(√5)) (secθ − cosecθ)
aii) Prove that: (√((1 + cosθ)/(1 − cosθ))) = cosecθ + cotθ, if cosθ ≠ 1
(b) Let R be a positive real number and let α satisfy the inequality
0 < α < 360. express the function 2sinθ + cosθ in the form Rsin(θ + α).
Hence, find the value of θ between 0 and 360 which satisfy the equation.
3cosθ + 6sinθ = 1
The angles A, B, C of a triangle ABC
satisfy 4cosAcosB + sin2A + sin2B +
sin2C = 4. Then which of the following
statements is/are correct?
(1) The triangle ABC is right angled
(2) The triangle ABC is isosceles
(3) The triangle ABC is neither
isosceles nor right angled
(4) The triangle ABC is equilateral
A large number of bullets are fired in
all direction with same speed u. The
maximum area on the ground covered
by these bullets will be
(1) π.(u^2 /g)
(2) π.(u^4 /g^2 )
(3) (π/4).(u^4 /g^2 )
(4) (π/2).(u^4 /g^2 )