Prove the identity $$$\frac{1-2 \sin ^{2} \theta}{1-\sin ^{2} \theta} \equiv 1-\tan ^{2} \theta$$$. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s21_qp_11 Year：2021 Question No：7(a)

Answer:

Reach $\frac{\cos ^{2} \theta-\sin ^{2} \theta}{\cos ^{2} \theta}$ or $\frac{1-\sin ^{2} \theta}{1-\sin ^{2} \theta}-\frac{\sin ^{2} \theta}{\cos ^{2} \theta}$ or $\frac{\sin ^{2} \theta+\cos ^{2} \theta}{\cos ^{2} \theta}-2 \tan ^{2} \theta$ or $\sec ^{2} \theta-\frac{2 \sin ^{2} \theta}{\cos ^{2} \theta}$ or $2-\sec ^{2} \theta$ or $\frac{\cos 2 \theta}{\cos ^{2} \theta}$
$1-\tan ^{2} \theta$

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