Question

solve the given question

Answer 1

sin Ф = cos Ф
sin Ф = sin(90° - Ф)
or Ф = 90°- Ф
or 2Ф = 90°
So, Ф =90°/2 = 45°

second method
Sin Ф = cos Ф
sinФ/cosФ = 1
tanФ = 1
tanФ = tan 45°
Ф = 45°

We Know that
Arithmetic Mean ≥ Geometric Mean
(a+1/a)/2≥sqrt(a×1/a)
a+1/a≥2sqrt(a×1/a)
a+1/a≥2
we know that
–1≤ sinθ ≤ 1
⇒–2 ≤ 2 sinθ ≤ 2
∴ The only possibility that the value of 2 sin θ can be a+1/a is when value of a+1/a is 2.
Now we check this value of a+1/a
Clearly, a+1/a is 2 only when a = 1
But a ≠ 1 ... (given)
Hence, the value of 2 sinθ can not be a+1/a.