The number of solutions of sin 7 x + cos 7 x = 1 , x ∈ [ 0 , 4 π ] is equal to

Step-by-step solution

We know that 0 ≤ sin 2 x ≤ 1 and 0 ≤ cos 2 x ≤ 1 Also, we know for a number which lie between 0 to 1 , higher the power of the number the less is its value. ⇒ sin 7 x ≤ sin 2 x ≤ 1       … 1 and cos 7 x ≤ cos 2 x ≤ 1       … 2 Also, we know that sin 2 x + cos 2 x = 1 This means the equality must hold for 1 and 2 ⇒ sin 7 x = sin 2 x and cos 7 x = cos 2 x ⇒ sin 2 x sin 5 x - 1 = 0 and cos 2 x cos 5 x - 1 = 0 &#