Prove the following:2 Marks Each
1. $cosec\theta \sqrt{1-co{s}^{2}\theta }=1$

2. $sec\theta \sqrt{1-si{n}^{2}\theta }=1$

3. $\left(cosec\theta -cot\theta {\right)}^{2}=\frac{1+cos\theta }{1-cos\theta }$

4. ${⟮sinA+cosecA⟯}^{2}+{⟮cosA+secA⟯}^{2}=7+ta{n}^{2}A+co{t}^{2}A$

5. $\left(cosecA–sinA\right)\left(secA–cosA\right)=\frac{1}{tanA+cotA}$

6. $\frac{sin\theta }{1-cos\theta }=cosec\theta +cot\theta$

7. $tan\theta -cot\theta =\frac{2si{n}^{2}\theta -1}{sin\theta cos\theta }$

Prove the following:3 Marks Each
1. $\sqrt{\frac{1+cos\theta }{1-cos\theta }}=cosec\theta +cot\theta$

2. $\sqrt{\frac{1-cos\theta }{1+cos\theta }}=cosec\theta -cot\theta$

3. $secA+tanA=\sqrt{\frac{1+sinA}{1-sinA}}$

4. $se{c}^{2}\theta -co{s}^{2}\theta =si{n}^{2}\theta \left(se{c}^{2}\theta +1\right)$

5. $co{s}^{4}\theta -co{s}^{2}\theta =si{n}^{4}\theta -si{n}^{2}\theta$