Prove that sec^2(θ) + cosec^2(θ) = sec^2(θ) * cosec^2(θ)
These problems can be tricky as they use unfamiliar trigonometric functions such as secant and cosecant. It is much easier to approach these problems by replacing these trigonometric functions with more familiar functions such as sine and cosine. Thus we can rewrite the problem to read: Prove that 1/cos2(θ) + 1/sin2(θ) = 1/cos2(θ) * 1/sin2(θ) , which is much more intuitive on how to solve. Rearranging this equation to become a well established identity would substantiate a proof for A-level Mathematics, and so multiplying both sides by sin2(θ) and cos2(θ) gives sin2(θ) + cos2(θ) = 1. This is the Pythagoras trigonometric identity and so we are done with the proof; (although a more rigorous proof could be accomplished by demonstrating he Pythagoras trigonometric identity using geometry).
