Mathematics

Mathematics

Problem

Verify the equality (sec⁡θ−tan⁡θ)(sec⁡θ+tan⁡θ)=1(\sec\theta-\tan\theta)(\sec\theta+\tan\theta)=1 for the specific value θ=45∘\theta=45^{\circ}. a. (i) Calculate the numerical values of sec⁡45∘\sec45^{\circ} and tan⁡45∘\tan45^{\circ}. b. (ii) Use these values to find the product (sec⁡45∘−tan⁡45∘)(sec⁡45∘+tan⁡45∘)(\sec45^{\circ}-\tan45^{\circ})(\sec45^{\circ}+\tan45^{\circ}) and show that it equals 11.

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