For , if , then the value of is equal…

MATHEMATICS · Single correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

For θ1,θ2,…,θn∈(0,π2)\theta_1,\theta_2,\ldots,\theta_n\in\left(0,\frac{\pi}{2}\right), if ln⁡(sec⁡θ1−tan⁡θ1)+ln⁡(sec⁡θ2−tan⁡θ2)+⋯+ln⁡(sec⁡θn−tan⁡θn)+ln⁡π=0\ln(\sec\theta_1-\tan\theta_1)+\ln(\sec\theta_2-\tan\theta_2)+\cdots+\ln(\sec\theta_n-\tan\theta_n)+\ln\pi=0, then the value of cos⁡((sec⁡θ1+tan⁡θ1)(sec⁡θ2+tan⁡θ2)⋯(sec⁡θn+tan⁡θn))\cos\left((\sec\theta_1+\tan\theta_1)(\sec\theta_2+\tan\theta_2)\cdots(\sec\theta_n+\tan\theta_n)\right) is equal to (1) cos⁡(1π)\cos\left(\frac{1}{\pi}\right) (2) −1-1 (3) 11 (4) 00

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