Question

The number of solutions for the equation sin 2x + cos 4x = 2 is

(a) 0

(b) 1

(c) 2

(d) ∞

Answer 1

Solution:

Given,

sin 2x + cos 4x = 2

sin 2x + [1 – 2 sin2(2x)] – 2 = 0 {since cos 2A = 1 – 2sin2A}

sin 2x -1 – 2 sin2(2x) = 0

Let sin 2x = t

t – 1 – 2t2 = 0

2t2 – t + 1 = 0

Using the quadratic formula,

t = [1 ± √(1 – 8)]/2(2)

t = (1 ± √-7)/4

sin 2x = (1 ± i√7)/4

Therefore, there is no solution to x.

Answer 2

Q) The number of solutions for the equation sin 2x + cos 4x = 2 is

(a) 0

(b) 1

(c) 2

(d) ∞

ANSWER:-

no solution the answer is be X .