To prove the equation, we start by evaluating the left side, which consists of four instances of tan(45°).
We know that:
- tan(45°) = 1
So, we can rewrite the left side:
tan(45°) × tan(45°) × tan(45°) × tan(45°) = 1 × 1 × 1 × 1 = 1.
Now, we need to evaluate the right side, which is 1/sin²(a).
The equation we need to check is:
1 = 1/sin²(a)
To solve this, we can multiply both sides by sin²(a):
1 × sin²(a) = 1
Which simplifies to:
sin²(a) = 1.
This equation holds true only when a = 90° (or multiples of π/2 in radians). In all other cases, sin²(a) will not equal 1.
Thus, the original equation proves true specifically at the point where a leads to sin(a) equating to 1 (i.e., when a = 90°). For cases where a cannot be 90°, the expressions diverge. Therefore, the equation may not hold universally without constraints on the angle a.