If cos x = sin y and cot (x - 40°) = tan (50° - y), then the value of x and y are:
x = 70°, y = 20°
x = 75°, y = 15°
x = 85°, y = 5°
x = 80°, y = 10°
If sin θ + sin2θ = 1, then the value of cos12 θ + 3 cos 10 θ + 3 cos8 θ + cos6 θ - 1 is
0
1
-1
2
A.
0
sinθ + sin2θ = 1
⟹ sinθ = 1 - sin2θ
⟹ sinθ = cos2θ ...(i)
cos12 θ + 3 cos 10 θ + 3 cos8 θ + cos6 θ - 1
= (cos 4θ + cos2θ)3 - 1
= (sin2θ + cos2θ)2 - 1
= (1)2 - 1
= 0
If x, y are positive acute angles x + y < 90° and sin (2x - 20°) = cos (2y + 20°), then the values of sec (x + y) is
1
0