To prove that:
tan(45) × tan(45) × tan(45) × tan(45) = 1 × sin(2a)
First, let’s simplify the left-hand side:
We know that:
tan(45) = 1
So, if we multiply tan(45) four times:
tan(45) × tan(45) × tan(45) × tan(45) = 1 × 1 × 1 × 1 = 1
Now, we have:
1 = 1 × sin(2a)
In order for this equation to hold true, it implies that:
sin(2a) must equal 1
Since sin(θ) reaches its maximum value of 1 when θ = 90°, this leads us to:
2a = 90°
To find ‘a’, we solve:
a = 45°
Thus, we’ve shown that under the condition where ‘a’ equals 45°, the equation holds true:
tan(45) × tan(45) × tan(45) × tan(45) = 1 × sin(2 × 45°)
This confirms our initial query, completing the proof!