Question

[sin47 degree/cos 43 degree]²+(cos 43 degree/sin 47 degree)²-4cos45 degree=0
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Answer 1

Answer✍

• We know that sin(90 - θ) = cosθ and similarly, cos(90 - θ) = sinθ

• Therefore in the given expression the sinθ's can be converted into cosθ to check if it's equal to the RHS which is 0.

Sin47° can be expressed as cos(90-47) or cos43°

→ (cos43°/cos43°)²+(cos43°/cos43°)² - 4 · cos²45°

→ 1 + 1 - 4 × (1/√2)² (∵ cos45° = 1/√2)

→ 2 - 4 × (1/2)

→ 2 - 2

→ 0

∴ LHS = RHS

Hence Proved.

[Note: You probably meant 4 cos²45° or 4 (cos45°)² instead of 4 cos45° as, if written otherwise the given equation would be untrue]

Hope this helps you!