If , then is equal to .

Question

If , then  is equal to .

Canvas Classes · Accepted Answer

🧠 Pair Up Complementary Angles, Then Use the Triple-Product Identity

The expression  has six factors. The angles  and  are complementary, so we can replace them with cosines:

.

So .

Now we have . The plan is to expand  using , multiply out, and use product-to-sum repeatedly until everything reduces to  and constants.

This is a multi-step grind. The first move (complementary-angle swap) is the key. Once that is done, the rest is mechanical.

🗺️ Working It Out

So the expression equals .

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