Answer the following:

MATHEMATICS · Subjective · CBSE · Mathematics · Introduction to Trigonometry · Introduction to Trigonometry

Problem

Answer the following: (i) State the fundamental identity involving sin⁡θ\sin \theta and cos⁡θ\cos \theta. (ii) Using the identity stated in part (i), derive the relation connecting 1+tan⁡2θ1+\tan^{2}\theta and sec⁡2θ\sec^{2}\theta. (iii) An angle θ\theta lies in the third quadrant. Explain, with reasons based on unit–circle coordinates, the signs of sin⁡θ\sin \theta, cos⁡θ\cos \theta and tan⁡θ\tan \theta. Hence determine whether sec⁡θ\sec \theta is positive or negative in this quadrant.

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